Category Archives: pow 典型形式

判定兩個冪零矩陣相似的充要條件。 Let and be nonzero matrices. (a) If , is it true that and are similar if and only if ? (b) If , is it true that and are similar if and only if ?

矩陣 相似於 等價於 相似於一實矩陣。 Let be an complex matrix. Show that is similar to a real matrix if and only if is similar to .

試寫出所有可能的四階冪零矩陣 (nilpotent) 的 Jordan 形式。 Determine all possible Jordan forms for a nilpotent matrix.

這是關於冪零矩陣的問題。 Let and be matrices. Does imply ?

若一矩陣的所有特徵值皆等於 ，則此矩陣相似於其逆矩陣。 Let be an matrix with characteristic polynomial . Show that is similar to its inverse.

這是 Jordan 典型形式的相似證明問題。 Let where . Show that is similar to .

這是有關可對角化矩陣的問題。 Let be a real matrix. If , show that is diagonalizable.

本週問題是關於 Jordan 典型形式的相似問題。 Let where . Show that is similar to .