Book to learn Advanced Linear Algebra and Matrix Theory
$begingroup$
I am looking for a book to learn Advanced Linear Algebra and Matrix Theory in detail.
Sheldon Axler :Doesn't cover matrix theory,Hoffman,Kunze:Doesn't have many exercises and examples on each of the topics
Please suggest some alternatives
Requisites: Theorems with proofs,easy ones left to reader,Enough examples,Good Exercises(with Hints if possible)
Topics to cover:
- Systems of Linear equations
- Diagonalization of a square matrix
- Vector Spaces
- Solutions of Linear Systems: Gaussian elimination
, Null Space and Range
, Rank and nullity, Consistency conditions in terms of rank
, General Solution of a linear system
, Elementary Row and Column operations
, Row Reduced Form
,Triangular Matrix Factorization
5.Important Subspaces associsted with a matrix: Range and Null space, Rank and Nullity,Rank Nullity theorem .
6.Orthogonality: Inner product, Inner product Spaces
, Cauchy – Schwarz inequality
, Norm
, Orthogonality
, Gram – Schmidt orthonormalization
, Orthonormal basis
, Expansion in terms of orthonormal basis – Fourier
series
, Orthogonal complement.
7.Eigenvalues and Eigenvectors
- Hermitian Matrices:Real symmetric and Hermitian Matrices
Properties of eigenvalues and eigenvectors.
9.General Matrices: The matrices $AA^T,A^TA$
Rank, Nullity, Range and Null Space of $AA^T,A^TA$
,Singular Value Decomposition.
10.Jordan Cnonical form:
Primary Decomposition Theorem
Nilpotent matrices
Canonical form for a nilpotent matrix
Mostly results on MSE said to follow Matrix Analysis-Horn,Johnson but the book does not cover all the topics in great detail.It focuses on more advanced topics.
Please suggest a book accordingly as I need to prepare for my exam.
linear-algebra matrices reference-request soft-question book-recommendation
asked Oct 6 '17 at 4:48
LearnmoreLearnmore
17.8k325106
$endgroup$
|
show 1 more comment
$begingroup$
I am looking for a book to learn Advanced Linear Algebra and Matrix Theory in detail.
Sheldon Axler :Doesn't cover matrix theory,Hoffman,Kunze:Doesn't have many exercises and examples on each of the topics
Please suggest some alternatives
Requisites: Theorems with proofs,easy ones left to reader,Enough examples,Good Exercises(with Hints if possible)
Topics to cover:
- Systems of Linear equations
- Diagonalization of a square matrix
- Vector Spaces
- Solutions of Linear Systems: Gaussian elimination
, Null Space and Range
, Rank and nullity, Consistency conditions in terms of rank
, General Solution of a linear system
, Elementary Row and Column operations
, Row Reduced Form
,Triangular Matrix Factorization
5.Important Subspaces associsted with a matrix: Range and Null space, Rank and Nullity,Rank Nullity theorem .
6.Orthogonality: Inner product, Inner product Spaces
, Cauchy – Schwarz inequality
, Norm
, Orthogonality
, Gram – Schmidt orthonormalization
, Orthonormal basis
, Expansion in terms of orthonormal basis – Fourier
series
, Orthogonal complement.
7.Eigenvalues and Eigenvectors
- Hermitian Matrices:Real symmetric and Hermitian Matrices
Properties of eigenvalues and eigenvectors.
9.General Matrices: The matrices $AA^T,A^TA$
Rank, Nullity, Range and Null Space of $AA^T,A^TA$
,Singular Value Decomposition.
10.Jordan Cnonical form:
Primary Decomposition Theorem
Nilpotent matrices
Canonical form for a nilpotent matrix
Mostly results on MSE said to follow Matrix Analysis-Horn,Johnson but the book does not cover all the topics in great detail.It focuses on more advanced topics.
Please suggest a book accordingly as I need to prepare for my exam.
linear-algebra matrices reference-request soft-question book-recommendation
asked Oct 6 '17 at 4:48
LearnmoreLearnmore
17.8k325106
$endgroup$
$begingroup$
Hoffman and Kunze
$endgroup$
– Bungo
Oct 6 '17 at 4:50
$begingroup$
Strang's texts also an option here (at least in terms of topics covered). Not the greatest for proof questions, but he has some interesting conceptual questions, I guess.
$endgroup$
– Omnomnomnom
Oct 6 '17 at 4:55
$begingroup$
Linear Algebra Done Right - Sheldon Axler
$endgroup$
– AnlamK
Oct 6 '17 at 4:57
1
$begingroup$
@AnlamK I would argue that that is a particularly bad recommendation for this purpose. My copy is at my office, but I don't think he covers Gaussian elimination, or really most of the things concerning Matrix theory.
$endgroup$
– Morgan Rodgers
Oct 6 '17 at 6:17
1
$begingroup$
Another possibility: take a look at Matrix Analysis and Applied Linear Algebra by Carl Meyer. I believe it covers all of the topics you listed, is quite detailed, and has lots of exercises. And (at least at the time I bought it), it comes bundled with a solution manual, as well as a CD-ROM containing a PDF copy of the book.
$endgroup$
– Bungo
Oct 6 '17 at 6:46
|
show 1 more comment
$begingroup$
I am looking for a book to learn Advanced Linear Algebra and Matrix Theory in detail.
Sheldon Axler :Doesn't cover matrix theory,Hoffman,Kunze:Doesn't have many exercises and examples on each of the topics
Please suggest some alternatives
Requisites: Theorems with proofs,easy ones left to reader,Enough examples,Good Exercises(with Hints if possible)
Topics to cover:
- Systems of Linear equations
- Diagonalization of a square matrix
- Vector Spaces
- Solutions of Linear Systems: Gaussian elimination
, Null Space and Range
, Rank and nullity, Consistency conditions in terms of rank
, General Solution of a linear system
, Elementary Row and Column operations
, Row Reduced Form
,Triangular Matrix Factorization
5.Important Subspaces associsted with a matrix: Range and Null space, Rank and Nullity,Rank Nullity theorem .
6.Orthogonality: Inner product, Inner product Spaces
, Cauchy – Schwarz inequality
, Norm
, Orthogonality
, Gram – Schmidt orthonormalization
, Orthonormal basis
, Expansion in terms of orthonormal basis – Fourier
series
, Orthogonal complement.
7.Eigenvalues and Eigenvectors
- Hermitian Matrices:Real symmetric and Hermitian Matrices
Properties of eigenvalues and eigenvectors.
9.General Matrices: The matrices $AA^T,A^TA$
Rank, Nullity, Range and Null Space of $AA^T,A^TA$
,Singular Value Decomposition.
10.Jordan Cnonical form:
Primary Decomposition Theorem
Nilpotent matrices
Canonical form for a nilpotent matrix
Mostly results on MSE said to follow Matrix Analysis-Horn,Johnson but the book does not cover all the topics in great detail.It focuses on more advanced topics.
Please suggest a book accordingly as I need to prepare for my exam.
linear-algebra matrices reference-request soft-question book-recommendation
asked Oct 6 '17 at 4:48
LearnmoreLearnmore
17.8k325106
$endgroup$
I am looking for a book to learn Advanced Linear Algebra and Matrix Theory in detail.
Sheldon Axler :Doesn't cover matrix theory,Hoffman,Kunze:Doesn't have many exercises and examples on each of the topics
Please suggest some alternatives
Requisites: Theorems with proofs,easy ones left to reader,Enough examples,Good Exercises(with Hints if possible)
Topics to cover:
- Systems of Linear equations
- Diagonalization of a square matrix
- Vector Spaces
- Solutions of Linear Systems: Gaussian elimination
, Null Space and Range
, Rank and nullity, Consistency conditions in terms of rank
, General Solution of a linear system
, Elementary Row and Column operations
, Row Reduced Form
,Triangular Matrix Factorization
5.Important Subspaces associsted with a matrix: Range and Null space, Rank and Nullity,Rank Nullity theorem .
6.Orthogonality: Inner product, Inner product Spaces
, Cauchy – Schwarz inequality
, Norm
, Orthogonality
, Gram – Schmidt orthonormalization
, Orthonormal basis
, Expansion in terms of orthonormal basis – Fourier
series
, Orthogonal complement.
7.Eigenvalues and Eigenvectors
- Hermitian Matrices:Real symmetric and Hermitian Matrices
Properties of eigenvalues and eigenvectors.
9.General Matrices: The matrices $AA^T,A^TA$
Rank, Nullity, Range and Null Space of $AA^T,A^TA$
,Singular Value Decomposition.
10.Jordan Cnonical form:
Primary Decomposition Theorem
Nilpotent matrices
Canonical form for a nilpotent matrix
Mostly results on MSE said to follow Matrix Analysis-Horn,Johnson but the book does not cover all the topics in great detail.It focuses on more advanced topics.
Please suggest a book accordingly as I need to prepare for my exam.
linear-algebra matrices reference-request soft-question book-recommendation
linear-algebra matrices reference-request soft-question book-recommendation
asked Oct 6 '17 at 4:48
LearnmoreLearnmore
17.8k325106
asked Oct 6 '17 at 4:48
LearnmoreLearnmore
17.8k325106
edited Oct 6 '17 at 6:23
Learnmore
asked Oct 6 '17 at 4:48
LearnmoreLearnmore
17.8k325106
asked Oct 6 '17 at 4:48
LearnmoreLearnmore
17.8k325106
asked Oct 6 '17 at 4:48
LearnmoreLearnmore
17.8k325106
17.8k325106
$begingroup$
Hoffman and Kunze
$endgroup$
– Bungo
Oct 6 '17 at 4:50
$begingroup$
Strang's texts also an option here (at least in terms of topics covered). Not the greatest for proof questions, but he has some interesting conceptual questions, I guess.
$endgroup$
– Omnomnomnom
Oct 6 '17 at 4:55
$begingroup$
Linear Algebra Done Right - Sheldon Axler
$endgroup$
– AnlamK
Oct 6 '17 at 4:57
1
$begingroup$
@AnlamK I would argue that that is a particularly bad recommendation for this purpose. My copy is at my office, but I don't think he covers Gaussian elimination, or really most of the things concerning Matrix theory.
$endgroup$
– Morgan Rodgers
Oct 6 '17 at 6:17
1
$begingroup$
Another possibility: take a look at Matrix Analysis and Applied Linear Algebra by Carl Meyer. I believe it covers all of the topics you listed, is quite detailed, and has lots of exercises. And (at least at the time I bought it), it comes bundled with a solution manual, as well as a CD-ROM containing a PDF copy of the book.
$endgroup$
– Bungo
Oct 6 '17 at 6:46
|
show 1 more comment
$begingroup$
Hoffman and Kunze
$endgroup$
– Bungo
Oct 6 '17 at 4:50
$begingroup$
Strang's texts also an option here (at least in terms of topics covered). Not the greatest for proof questions, but he has some interesting conceptual questions, I guess.
$endgroup$
– Omnomnomnom
Oct 6 '17 at 4:55
$begingroup$
Linear Algebra Done Right - Sheldon Axler
$endgroup$
– AnlamK
Oct 6 '17 at 4:57
1
$begingroup$
@AnlamK I would argue that that is a particularly bad recommendation for this purpose. My copy is at my office, but I don't think he covers Gaussian elimination, or really most of the things concerning Matrix theory.
$endgroup$
– Morgan Rodgers
Oct 6 '17 at 6:17
1
$begingroup$
Another possibility: take a look at Matrix Analysis and Applied Linear Algebra by Carl Meyer. I believe it covers all of the topics you listed, is quite detailed, and has lots of exercises. And (at least at the time I bought it), it comes bundled with a solution manual, as well as a CD-ROM containing a PDF copy of the book.
$endgroup$
– Bungo
Oct 6 '17 at 6:46
$begingroup$
Hoffman and Kunze
$endgroup$
– Bungo
Oct 6 '17 at 4:50
$begingroup$
Hoffman and Kunze
$endgroup$
– Bungo
Oct 6 '17 at 4:50
$begingroup$
Strang's texts also an option here (at least in terms of topics covered). Not the greatest for proof questions, but he has some interesting conceptual questions, I guess.
$endgroup$
– Omnomnomnom
Oct 6 '17 at 4:55
$begingroup$
Strang's texts also an option here (at least in terms of topics covered). Not the greatest for proof questions, but he has some interesting conceptual questions, I guess.
$endgroup$
– Omnomnomnom
Oct 6 '17 at 4:55
$begingroup$
Linear Algebra Done Right - Sheldon Axler
$endgroup$
– AnlamK
Oct 6 '17 at 4:57
$begingroup$
Linear Algebra Done Right - Sheldon Axler
$endgroup$
– AnlamK
Oct 6 '17 at 4:57
1
1
$begingroup$
@AnlamK I would argue that that is a particularly bad recommendation for this purpose. My copy is at my office, but I don't think he covers Gaussian elimination, or really most of the things concerning Matrix theory.
$endgroup$
– Morgan Rodgers
Oct 6 '17 at 6:17
$begingroup$
@AnlamK I would argue that that is a particularly bad recommendation for this purpose. My copy is at my office, but I don't think he covers Gaussian elimination, or really most of the things concerning Matrix theory.
$endgroup$
– Morgan Rodgers
Oct 6 '17 at 6:17
1
1
$begingroup$
Another possibility: take a look at Matrix Analysis and Applied Linear Algebra by Carl Meyer. I believe it covers all of the topics you listed, is quite detailed, and has lots of exercises. And (at least at the time I bought it), it comes bundled with a solution manual, as well as a CD-ROM containing a PDF copy of the book.
$endgroup$
– Bungo
Oct 6 '17 at 6:46
$begingroup$
Another possibility: take a look at Matrix Analysis and Applied Linear Algebra by Carl Meyer. I believe it covers all of the topics you listed, is quite detailed, and has lots of exercises. And (at least at the time I bought it), it comes bundled with a solution manual, as well as a CD-ROM containing a PDF copy of the book.
$endgroup$
– Bungo
Oct 6 '17 at 6:46
|
show 1 more comment
2 Answers
2
active
oldest
votes
$begingroup$
I highly recommend A Second Course in Linear Algebra, by Garcia and Horn.
Review by:
MAA;
Nicholas Higham.
answered Dec 20 '18 at 18:48
Pietro PaparellaPietro Paparella
1,594615
$endgroup$
add a comment |
$begingroup$
The Linear Algebra a Beginning Graduate Student Ought to Know has a pretty good presentation of all this material. It's got some less standard notations and terminology, but it's a good, detailed look at advanced linear algebra and matrix theory.
answered Dec 20 '18 at 20:02
AlexanderJ93AlexanderJ93
6,193823
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2459925%2fbook-to-learn-advanced-linear-algebra-and-matrix-theory%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I highly recommend A Second Course in Linear Algebra, by Garcia and Horn.
Review by:
MAA;
Nicholas Higham.
answered Dec 20 '18 at 18:48
Pietro PaparellaPietro Paparella
1,594615
$endgroup$
add a comment |
$begingroup$
I highly recommend A Second Course in Linear Algebra, by Garcia and Horn.
Review by:
MAA;
Nicholas Higham.
answered Dec 20 '18 at 18:48
Pietro PaparellaPietro Paparella
1,594615
$endgroup$
add a comment |
$begingroup$
I highly recommend A Second Course in Linear Algebra, by Garcia and Horn.
Review by:
MAA;
Nicholas Higham.
answered Dec 20 '18 at 18:48
Pietro PaparellaPietro Paparella
1,594615
$endgroup$
I highly recommend A Second Course in Linear Algebra, by Garcia and Horn.
Review by:
MAA;
Nicholas Higham.
answered Dec 20 '18 at 18:48
Pietro PaparellaPietro Paparella
1,594615
answered Dec 20 '18 at 18:48
Pietro PaparellaPietro Paparella
1,594615
answered Dec 20 '18 at 18:48
Pietro PaparellaPietro Paparella
1,594615
answered Dec 20 '18 at 18:48
Pietro PaparellaPietro Paparella
1,594615
1,594615
add a comment |
add a comment |
$begingroup$
The Linear Algebra a Beginning Graduate Student Ought to Know has a pretty good presentation of all this material. It's got some less standard notations and terminology, but it's a good, detailed look at advanced linear algebra and matrix theory.
answered Dec 20 '18 at 20:02
AlexanderJ93AlexanderJ93
6,193823
$endgroup$
add a comment |
$begingroup$
The Linear Algebra a Beginning Graduate Student Ought to Know has a pretty good presentation of all this material. It's got some less standard notations and terminology, but it's a good, detailed look at advanced linear algebra and matrix theory.
answered Dec 20 '18 at 20:02
AlexanderJ93AlexanderJ93
6,193823
$endgroup$
add a comment |
$begingroup$
The Linear Algebra a Beginning Graduate Student Ought to Know has a pretty good presentation of all this material. It's got some less standard notations and terminology, but it's a good, detailed look at advanced linear algebra and matrix theory.
answered Dec 20 '18 at 20:02
AlexanderJ93AlexanderJ93
6,193823
$endgroup$
The Linear Algebra a Beginning Graduate Student Ought to Know has a pretty good presentation of all this material. It's got some less standard notations and terminology, but it's a good, detailed look at advanced linear algebra and matrix theory.
answered Dec 20 '18 at 20:02
AlexanderJ93AlexanderJ93
6,193823
answered Dec 20 '18 at 20:02
AlexanderJ93AlexanderJ93
6,193823
answered Dec 20 '18 at 20:02
AlexanderJ93AlexanderJ93
6,193823
answered Dec 20 '18 at 20:02
AlexanderJ93AlexanderJ93
6,193823
6,193823
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2459925%2fbook-to-learn-advanced-linear-algebra-and-matrix-theory%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Hoffman and Kunze
$endgroup$
– Bungo
Oct 6 '17 at 4:50
$begingroup$
Strang's texts also an option here (at least in terms of topics covered). Not the greatest for proof questions, but he has some interesting conceptual questions, I guess.
$endgroup$
– Omnomnomnom
Oct 6 '17 at 4:55
$begingroup$
Linear Algebra Done Right - Sheldon Axler
$endgroup$
– AnlamK
Oct 6 '17 at 4:57
1
$begingroup$
@AnlamK I would argue that that is a particularly bad recommendation for this purpose. My copy is at my office, but I don't think he covers Gaussian elimination, or really most of the things concerning Matrix theory.
$endgroup$
– Morgan Rodgers
Oct 6 '17 at 6:17
1
$begingroup$
Another possibility: take a look at Matrix Analysis and Applied Linear Algebra by Carl Meyer. I believe it covers all of the topics you listed, is quite detailed, and has lots of exercises. And (at least at the time I bought it), it comes bundled with a solution manual, as well as a CD-ROM containing a PDF copy of the book.
$endgroup$
– Bungo
Oct 6 '17 at 6:46