To find the nullity of a matrix.
Let $x = [ x_1 ,x_2, x_3]^T in mathbb R^3 $( T denotes the transpose) be a non zero vector and A $= x(x^T)/(x^T)x$. Then What is the nullity of A?
$xx^T$ is 3*3 matrix with nullity 2 and $(x^T)x$ is 1*1 nonzero matrix. A is defined as division of $xx^T$ and $(x^T)x$. Matrix division is not defined then how to solve this problem?
linear-algebra matrices
edited Nov 23 at 5:40
Shubham
1,5921519
asked Nov 23 at 5:23
Mathsaddict
1308
add a comment |
Let $x = [ x_1 ,x_2, x_3]^T in mathbb R^3 $( T denotes the transpose) be a non zero vector and A $= x(x^T)/(x^T)x$. Then What is the nullity of A?
$xx^T$ is 3*3 matrix with nullity 2 and $(x^T)x$ is 1*1 nonzero matrix. A is defined as division of $xx^T$ and $(x^T)x$. Matrix division is not defined then how to solve this problem?
linear-algebra matrices
edited Nov 23 at 5:40
Shubham
1,5921519
asked Nov 23 at 5:23
Mathsaddict
1308
1
A $1 times 1$ matrix can be treated as a scalar.
– Anurag A
Nov 23 at 5:24
Please see math.meta.stackexchange.com/questions/5020
– Lord Shark the Unknown
Nov 23 at 5:24
@Anurag A I didn't know this. Can 1*1 matrices be treated as scalars in all type of problems?
– Mathsaddict
Nov 23 at 5:33
@Mathsaddict $1times 1$ matrix is itself a scalar always if entries are in field.
– Shubham
Nov 23 at 5:40
add a comment |
Let $x = [ x_1 ,x_2, x_3]^T in mathbb R^3 $( T denotes the transpose) be a non zero vector and A $= x(x^T)/(x^T)x$. Then What is the nullity of A?
$xx^T$ is 3*3 matrix with nullity 2 and $(x^T)x$ is 1*1 nonzero matrix. A is defined as division of $xx^T$ and $(x^T)x$. Matrix division is not defined then how to solve this problem?
linear-algebra matrices
edited Nov 23 at 5:40
Shubham
1,5921519
asked Nov 23 at 5:23
Mathsaddict
1308
Let $x = [ x_1 ,x_2, x_3]^T in mathbb R^3 $( T denotes the transpose) be a non zero vector and A $= x(x^T)/(x^T)x$. Then What is the nullity of A?
$xx^T$ is 3*3 matrix with nullity 2 and $(x^T)x$ is 1*1 nonzero matrix. A is defined as division of $xx^T$ and $(x^T)x$. Matrix division is not defined then how to solve this problem?
linear-algebra matrices
linear-algebra matrices
edited Nov 23 at 5:40
Shubham
1,5921519
asked Nov 23 at 5:23
Mathsaddict
1308
edited Nov 23 at 5:40
Shubham
1,5921519
asked Nov 23 at 5:23
Mathsaddict
1308
edited Nov 23 at 5:40
Shubham
1,5921519
edited Nov 23 at 5:40
Shubham
1,5921519
edited Nov 23 at 5:40
Shubham
1,5921519
1,5921519
asked Nov 23 at 5:23
Mathsaddict
1308
asked Nov 23 at 5:23
Mathsaddict
1308
asked Nov 23 at 5:23
Mathsaddict
1308
1308
1
A $1 times 1$ matrix can be treated as a scalar.
– Anurag A
Nov 23 at 5:24
Please see math.meta.stackexchange.com/questions/5020
– Lord Shark the Unknown
Nov 23 at 5:24
@Anurag A I didn't know this. Can 1*1 matrices be treated as scalars in all type of problems?
– Mathsaddict
Nov 23 at 5:33
@Mathsaddict $1times 1$ matrix is itself a scalar always if entries are in field.
– Shubham
Nov 23 at 5:40
add a comment |
1
A $1 times 1$ matrix can be treated as a scalar.
– Anurag A
Nov 23 at 5:24
Please see math.meta.stackexchange.com/questions/5020
– Lord Shark the Unknown
Nov 23 at 5:24
@Anurag A I didn't know this. Can 1*1 matrices be treated as scalars in all type of problems?
– Mathsaddict
Nov 23 at 5:33
@Mathsaddict $1times 1$ matrix is itself a scalar always if entries are in field.
– Shubham
Nov 23 at 5:40
1
1
A $1 times 1$ matrix can be treated as a scalar.
– Anurag A
Nov 23 at 5:24
A $1 times 1$ matrix can be treated as a scalar.
– Anurag A
Nov 23 at 5:24
Please see math.meta.stackexchange.com/questions/5020
– Lord Shark the Unknown
Nov 23 at 5:24
Please see math.meta.stackexchange.com/questions/5020
– Lord Shark the Unknown
Nov 23 at 5:24
@Anurag A I didn't know this. Can 1*1 matrices be treated as scalars in all type of problems?
– Mathsaddict
Nov 23 at 5:33
@Anurag A I didn't know this. Can 1*1 matrices be treated as scalars in all type of problems?
– Mathsaddict
Nov 23 at 5:33
@Mathsaddict $1times 1$ matrix is itself a scalar always if entries are in field.
– Shubham
Nov 23 at 5:40
@Mathsaddict $1times 1$ matrix is itself a scalar always if entries are in field.
– Shubham
Nov 23 at 5:40
add a comment |
1 Answer
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That's not a matrix division. In fact $x^Tx=||x||_2^2$ where $||x||_p$ is the $p$-norm. The nullity of $A$ would be $${winBbb R^3|w^Tx=0}$$which is a subspace of $Bbb R^3$ of dimension $2$.
answered Nov 24 at 12:46
Mostafa Ayaz
13.7k3836
add a comment |
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That's not a matrix division. In fact $x^Tx=||x||_2^2$ where $||x||_p$ is the $p$-norm. The nullity of $A$ would be $${winBbb R^3|w^Tx=0}$$which is a subspace of $Bbb R^3$ of dimension $2$.
answered Nov 24 at 12:46
Mostafa Ayaz
13.7k3836
add a comment |
That's not a matrix division. In fact $x^Tx=||x||_2^2$ where $||x||_p$ is the $p$-norm. The nullity of $A$ would be $${winBbb R^3|w^Tx=0}$$which is a subspace of $Bbb R^3$ of dimension $2$.
answered Nov 24 at 12:46
Mostafa Ayaz
13.7k3836
add a comment |
That's not a matrix division. In fact $x^Tx=||x||_2^2$ where $||x||_p$ is the $p$-norm. The nullity of $A$ would be $${winBbb R^3|w^Tx=0}$$which is a subspace of $Bbb R^3$ of dimension $2$.
answered Nov 24 at 12:46
Mostafa Ayaz
13.7k3836
That's not a matrix division. In fact $x^Tx=||x||_2^2$ where $||x||_p$ is the $p$-norm. The nullity of $A$ would be $${winBbb R^3|w^Tx=0}$$which is a subspace of $Bbb R^3$ of dimension $2$.
answered Nov 24 at 12:46
Mostafa Ayaz
13.7k3836
answered Nov 24 at 12:46
Mostafa Ayaz
13.7k3836
answered Nov 24 at 12:46
Mostafa Ayaz
13.7k3836
answered Nov 24 at 12:46
Mostafa Ayaz
13.7k3836
13.7k3836
add a comment |
add a comment |
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1
A $1 times 1$ matrix can be treated as a scalar.
– Anurag A
Nov 23 at 5:24
Please see math.meta.stackexchange.com/questions/5020
– Lord Shark the Unknown
Nov 23 at 5:24
@Anurag A I didn't know this. Can 1*1 matrices be treated as scalars in all type of problems?
– Mathsaddict
Nov 23 at 5:33
@Mathsaddict $1times 1$ matrix is itself a scalar always if entries are in field.
– Shubham
Nov 23 at 5:40