Schur product decomposition of Doubly stochastic matrix
It is true that for any unitary matrix $U$ a Schur product of the following form
$$A=U^*circ U$$
,where $U^*$ is the complex conjugate of $U$, is a doubly stochastic matrix. However, is the converse of this fact true? In other words, for arbitrary doubly stochastic matrix $A$, does there exist a unitary matrix such that $A=U^*circ U$ holds?
matrix-decomposition
asked Nov 28 '18 at 5:27
generic propertiesgeneric properties
447217
add a comment |
It is true that for any unitary matrix $U$ a Schur product of the following form
$$A=U^*circ U$$
,where $U^*$ is the complex conjugate of $U$, is a doubly stochastic matrix. However, is the converse of this fact true? In other words, for arbitrary doubly stochastic matrix $A$, does there exist a unitary matrix such that $A=U^*circ U$ holds?
matrix-decomposition
asked Nov 28 '18 at 5:27
generic propertiesgeneric properties
447217
add a comment |
It is true that for any unitary matrix $U$ a Schur product of the following form
$$A=U^*circ U$$
,where $U^*$ is the complex conjugate of $U$, is a doubly stochastic matrix. However, is the converse of this fact true? In other words, for arbitrary doubly stochastic matrix $A$, does there exist a unitary matrix such that $A=U^*circ U$ holds?
matrix-decomposition
asked Nov 28 '18 at 5:27
generic propertiesgeneric properties
447217
It is true that for any unitary matrix $U$ a Schur product of the following form
$$A=U^*circ U$$
,where $U^*$ is the complex conjugate of $U$, is a doubly stochastic matrix. However, is the converse of this fact true? In other words, for arbitrary doubly stochastic matrix $A$, does there exist a unitary matrix such that $A=U^*circ U$ holds?
matrix-decomposition
matrix-decomposition
asked Nov 28 '18 at 5:27
generic propertiesgeneric properties
447217
asked Nov 28 '18 at 5:27
generic propertiesgeneric properties
447217
edited Nov 28 '18 at 5:46
generic properties
asked Nov 28 '18 at 5:27
generic propertiesgeneric properties
447217
asked Nov 28 '18 at 5:27
generic propertiesgeneric properties
447217
asked Nov 28 '18 at 5:27
generic propertiesgeneric properties
447217
447217
add a comment |
add a comment |
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