→ iyenn:推~~ 04/15 23:59
推 ruby791104:謝謝s大，我再去研究研究！ 04/16 00:15
※ 引述《ruby791104 (阿年：）)》之銘言：
: 1.Show that A and A^T have the same eigenvalues. Do they necessarily have the
: same eigenvectors? Explain.
: 2.Let A be a 2 * 2 matrix. If tr(A) = 8 and det(A) = 12, what are the
: eigenvalues of A?
: 3.Let A be a nondefective n * n matrix with diagonalizing matrix X. Show that
: the matrix Y = (X^-1)^T diagonalizes A^T.
: 4.Let A be a diagonalizable matrix whose eigenvalues are all either 1 or -1.
: Show that A^-1 = A.
since A is diagonalizable, so there is P , P is invertible
such that P^(-1)AP =D, where D is diagonal matrix whose element are
all either 1 of -1
and note that D^2 = I => D^(-1)=D
so, A = PDP^(-1)
=> A^(-1) = PD^(-1)P^(-1) = PDP^(-1) = A.
應該是這樣囉
: 5.Find a matrix B such that B^2 = A.
: ┌ ┐
: ｜ 2 1｜
: A = ｜ ｜
: ｜-2 -1｜
: └ ┘
: 可以教我一下怎麼做嗎？
: 麻煩各位好心的大大了（鞠躬
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