Tag Archives: 可交換矩陣

這是網友范智忠提供的問題。 Let and be matrices. If , show that .

找出所有的可交換矩陣。 Find all matrices commuting with , where is the matrix all elements of which are equal to .

若對角矩陣有相異對角元與某個矩陣是可交換的，則該矩陣也是對角矩陣。 Prove the following statements. (a) Let , where are distinct. If , then is a diagonal matrix. (b) Let , where are distinct and nonzero, and be an matrix, where . If and , then .

證明可交換矩陣的一個充要條件。 Let and be matrices. Suppose that the eigenvectors of span and have distinct eigenvalues. Show that if and only if and have the same set of eigenvectors (with possibly different eigenvalues).

計算可交換矩陣構成的分塊矩陣的特徵值。 Let and be matrix. If , find the eigenvalues of .

這是可交換矩陣的秩不等式證明問題。 Let and be matrices. If , show that .