Tag Archives: 正規矩陣

證明 為正規矩陣 (normal matrix) 是一個充分條件。 Let and be normal matrices such that , where denotes the column space of . Prove that is a normal matrix. Note that is a normal matrix if .

任一正規矩陣 (normal matrix) 可表示為一個正規矩陣的平方。 Let be a normal matrix, i.e., . Prove that there exists a normal matrix such that .

關於兩個正規矩陣之積為正規矩陣的一個充分條件。 Let and be normal matrices. If is normal, show that is normal.

這是廣義化正規可交換矩陣問題。 Let and be normal matrices. If , show that .

這是正規矩陣的一個充要條件證明問題。 Prove that is a normal matrix if and only if , where is a unitary matrix.

這是關於正規可交換矩陣的問題。 If and are normal matrices and , show that , , and is a normal matrix.

這是運用正規矩陣的一個證明問題。 Let be an nonsingular matrix such that for some . Show that .

這是正規矩陣 (normal matrix) 的界定問題：若 的任一特徵向量是 的特徵向量，則 是正規矩陣，反之亦然。 Let be an matrix. Show that is normal if and only if any eigenvector of is an eigenvector of .