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A and B are two noncommuting Hermitian matrices:AB−BA=iCProve t... | Filo

A and B are two noncommuting Hermitian matrices:AB−BA=iCProve t... | Filo

5.3K views10 months ago

SOLVED: If A âˆˆ C^n is Hermitian, show that the rank of A is equal to the number of nonzero eigenvalues of A but that this is not generally true for non-Hermitian matrices.Show that A is Hermitian if and only if iA is skew-Hermitian. Deduce that the eigenvalues of a skew-Hermitian matrix are all pure imaginary and that the eigenvalues of the square of a skew-Hermitian matrix are real and nonpositive.Is a similar 4x4 Hermitian matrix necessarily Hermitian? What if M is a similarity matrix?Let AB

SOLVED: If A âˆˆ C^n is Hermitian, show that the rank of A is equal to the number of nonzero eigenvalues of A but that this is not generally true for non-Hermitian matrices.Show that A is Hermitian if and only if iA is skew-Hermitian. Deduce that the eigenvalues of a skew-Hermitian matrix are all pure imaginary and that the eigenvalues of the square of a skew-Hermitian matrix are real and nonpositive.Is a similar 4x4 Hermitian matrix necessarily Hermitian? What if M is a similarity matrix?Let AB

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