f*******g
发帖数: 55 | 1 Suppose A, B, and C are real, symmetric, and positive semi-definite matrices
. Is the matrix
ABC + C'B'A'
also positive semi-definite? (Here ' means transpose)
Thanks! | q********e
发帖数: 1255 | 2 no.
it's known that A\geq 0, B\geq 0 does not imply AB+BA\geq 0.
take C=I.
matrices
【在 f*******g 的大作中提到】
: Suppose A, B, and C are real, symmetric, and positive semi-definite matrices
: . Is the matrix
: ABC + C'B'A'
: also positive semi-definite? (Here ' means transpose)
: Thanks!
| q********e
发帖数: 1255 | 3 特征值非负不必正半定，对称性重要。
the classical example:
A=(1 2; 2 5);
B=(1 -1; -1 2); |
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