do the eigen values of hermittian matrix positive real nos.?

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do the eigen values of hermittian matrix positive real nos.?

2006-09-07 05:25:22 · 3 answers · asked by chemical engineer 1 in Science & Mathematics ➔ Mathematics

3 answers

Actually, this is not necessarily the case. It *is* true if the matrix is positive definite. It is also true that the eigenvalues have to be *real*, but it is possible for them to be negative. For example, the negative of the identity is hermitian, but has negative eigenvalues.

2006-09-07 08:13:35 · answer #1 · answered by mathematician 7 · 1⤊ 0⤋

yes... It turns out that this has great applications in the world of quantum mechanics.

2006-09-07 12:30:57 · answer #2 · answered by farrell_stu 4 · 0⤊ 1⤋

yes

2006-09-07 12:27:42 · answer #3 · answered by s_e_e 4 · 0⤊ 1⤋