0
$\begingroup$

If I multiply a Hurwitz matrix (real part of eigenvalues are negative) with a diagonal positive definite matrix, does the product still remain as Hurwitz matrix?

$\endgroup$
  • $\begingroup$ What is your definition of a Hurwitz matrix? $\endgroup$ – Arman Malekzadeh Jun 18 '17 at 6:55
  • $\begingroup$ A matrix is said to be Hurwitz iff its eigenvalues have a strictly negative real part. $\endgroup$ – palas Jun 18 '17 at 7:27
0
$\begingroup$

How about $$A=\pmatrix{1&1\\-4&-3}$$ and $$B=\pmatrix{4&0\\0&1}.$$ Then $A$ has repeated eigenvalues $-1$ so is Hurwitz, but $BA$ has positive trace so isn't.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.