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Is a square zero matrix positive semidefinite?
Algorithm for generating positive semidefinite matricesinequality-positive semidefinite matricesProve that every positive semidefinite matrix has nonnegative eigenvaluesEigenvalues and positive semidefiniteness of a special matrixHow to make a matrix positive semidefinite?Singularity positive semidefiniteSemidefinite matrix or indefinite?Can strict positive square matrix contain non zero same eigenvaluesThe square root of a positive semidefinite matrixSum of rank 1 positive semidefinite and negative semidefinite matrices
$begingroup$
Does the fact that a square zero matrix contains non-negative eigenvalues (zeros) make it proper to say it is positive semidefinite?
linear-algebra matrices positive-semidefinite
asked 4 hours ago
KayKay
617
$endgroup$
add a comment |
$begingroup$
Does the fact that a square zero matrix contains non-negative eigenvalues (zeros) make it proper to say it is positive semidefinite?
linear-algebra matrices positive-semidefinite
asked 4 hours ago
KayKay
617
$endgroup$
add a comment |
$begingroup$
Does the fact that a square zero matrix contains non-negative eigenvalues (zeros) make it proper to say it is positive semidefinite?
linear-algebra matrices positive-semidefinite
asked 4 hours ago
KayKay
617
$endgroup$
Does the fact that a square zero matrix contains non-negative eigenvalues (zeros) make it proper to say it is positive semidefinite?
linear-algebra matrices positive-semidefinite
linear-algebra matrices positive-semidefinite
asked 4 hours ago
KayKay
617
asked 4 hours ago
KayKay
617
edited 3 hours ago
Kay
asked 4 hours ago
KayKay
617
asked 4 hours ago
KayKay
617
asked 4 hours ago
KayKay
617
617
add a comment |
add a comment |
2 Answers
2
active
oldest
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$begingroup$
The $n times n$ zero matrix is positive semidefinite and negative semidefinite.
answered 4 hours ago
Gary MoonGary Moon
31613
$endgroup$
add a comment |
$begingroup$
"When in doubt, go back to the basic definitions"! The definition of "positive semi-definite" is "all eigen-values are non-negative". The eigenvalues or the zero matrix are all 0 so, yes, the zero matrix is positive semi-definite. And, as Gary Moon said, it is also negative semi-definite.
answered 3 hours ago
user247327user247327
11.4k1516
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The $n times n$ zero matrix is positive semidefinite and negative semidefinite.
answered 4 hours ago
Gary MoonGary Moon
31613
$endgroup$
add a comment |
$begingroup$
The $n times n$ zero matrix is positive semidefinite and negative semidefinite.
answered 4 hours ago
Gary MoonGary Moon
31613
$endgroup$
add a comment |
$begingroup$
The $n times n$ zero matrix is positive semidefinite and negative semidefinite.
answered 4 hours ago
Gary MoonGary Moon
31613
$endgroup$
The $n times n$ zero matrix is positive semidefinite and negative semidefinite.
answered 4 hours ago
Gary MoonGary Moon
31613
answered 4 hours ago
Gary MoonGary Moon
31613
answered 4 hours ago
Gary MoonGary Moon
31613
answered 4 hours ago
Gary MoonGary Moon
31613
31613
add a comment |
add a comment |
$begingroup$
"When in doubt, go back to the basic definitions"! The definition of "positive semi-definite" is "all eigen-values are non-negative". The eigenvalues or the zero matrix are all 0 so, yes, the zero matrix is positive semi-definite. And, as Gary Moon said, it is also negative semi-definite.
answered 3 hours ago
user247327user247327
11.4k1516
$endgroup$
add a comment |
$begingroup$
"When in doubt, go back to the basic definitions"! The definition of "positive semi-definite" is "all eigen-values are non-negative". The eigenvalues or the zero matrix are all 0 so, yes, the zero matrix is positive semi-definite. And, as Gary Moon said, it is also negative semi-definite.
answered 3 hours ago
user247327user247327
11.4k1516
$endgroup$
add a comment |
$begingroup$
"When in doubt, go back to the basic definitions"! The definition of "positive semi-definite" is "all eigen-values are non-negative". The eigenvalues or the zero matrix are all 0 so, yes, the zero matrix is positive semi-definite. And, as Gary Moon said, it is also negative semi-definite.
answered 3 hours ago
user247327user247327
11.4k1516
$endgroup$
"When in doubt, go back to the basic definitions"! The definition of "positive semi-definite" is "all eigen-values are non-negative". The eigenvalues or the zero matrix are all 0 so, yes, the zero matrix is positive semi-definite. And, as Gary Moon said, it is also negative semi-definite.
answered 3 hours ago
user247327user247327
11.4k1516
answered 3 hours ago
user247327user247327
11.4k1516
answered 3 hours ago
user247327user247327
11.4k1516
answered 3 hours ago
user247327user247327
11.4k1516
11.4k1516
add a comment |
add a comment |
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