申論題內容
10. (10%) How many of the following five statements are correct? ________
ㆍLet A be an n x n rational matrix. If the rational n-tuple vector space Qn" is the direct sum of the eigenspaces of A, then A can be diagonalized.
ㆍIf A is an n x n complex matrix with A*A = AA*, then the eigenspaces of A* equal the eigenspaces of A. If A is an n x n real matrix with At = A, then the characteristic polynomial of A can be written as a product of degree-one polynomials with real coefficients.
ㆍ If A is an n x n complex matrix with At = A, then all eigenvalues of A are real.
ㆍIf A and B are unitarily equivalent n x n complex matrices, then the trace of A*A equals the trace of B*B.
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