[理工] [線代]-eigenvalue證明&計算
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.
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？
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