Tag Archives: 相似

證明兩個冪等 (idempotent) 矩陣有相同秩的一個充分條件。 If is an matrix, a vector is said to be a fixed point of if . Let and be idempotent matrices, i.e., and . If the zero vector is the only fixed point of , show that … Continue reading →

證明兩個冪等 (idempotent) 矩陣相似的一個充要條件是它們有相同的秩。 Let and be idempotent matrices, i.e., and . Show that is similar to if and only if .

證明不存在恆定相似變換矩陣使任一矩陣相似於其轉置。 Prove that there is no nonsingular matrix such that for every matrix , .

這是證明兩分塊矩陣相似。 Let and be matrices. Show that matrix is similar to matrix , where .

這是關於在複數系和實數系的矩陣相似性問題。 Let and be real matrices. Show that if , where is a complex matrix, then there exists a real matrix such that . That is, if two real square matrices are similar over , then they must be similar … Continue reading →