準對角矩陣(quasi-diagonal matrix),亦稱準對角形矩陣.一種特殊矩陣。
基本介紹
- 中文名:準對角矩陣
- 外文名:quasi﹣diagonal matrix
- 別名:準對角形矩陣
定義,性質,
定義
準對煮葛棗員角矩陣(quasi-diagonal matrix)亦稱準對角形矩陣,一種特殊矩陣。即形如
![](/img/9/32e/wZ2NnLxImZ0ITZxgzNzMjN1kjZyIDZhZTNiFWOwUmYyYTZxU2LhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
的矩陣,其中Ai是ni×ni矩陣幾嘗趨(i=1,2, … ,l),通常稱為準對角矩陣。
性質
對於漿鴉煉兩個有相同分塊的準對角矩陣
A=
, B=
,
![](/img/d/fe2/wZ2NnL0cjMkZTM2UjZmBjN0gTNzUWZxgzNmFDO0MWO2IGNiZzLhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
![](/img/5/262/wZ2NnLhdTYhhjY0MzNlRWYjBDNjFmZkNGMiZzNjJzNxYzN0czLhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
(1)它們的和仍為同形準對角矩陣
A+B=![](/img/3/92a/wZ2NnLlFzNklDNhlTMwQDOxEGMwETNzIWNwQGMilzY3gzMjRzLhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
![](/img/3/92a/wZ2NnLlFzNklDNhlTMwQDOxEGMwETNzIWNwQGMilzY3gzMjRzLhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
(2)它們的積仍為同形準對角籃勸矩陣
AB=![](/img/e/52b/wZ2NnL3QGMzMWZxMDZxI2YhFzMiFjNmJDOkRmMidDNjRjM2E2LhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
![](/img/e/52b/wZ2NnL3QGMzMWZxMDZxI2YhFzMiFjNmJDOkRmMidDNjRjM2E2LhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
(3)一個數與準對角矩陣的乘積仍為同形準對角矩陣
kA=![](/img/b/64e/wZ2NnLxY2N2EWZ0YjN5EWYlJzYxkzYkRGOwIWY0ETNlVzNxQ2LhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
![](/img/b/64e/wZ2NnLxY2N2EWZ0YjN5EWYlJzYxkzYkRGOwIWY0ETNlVzNxQ2LhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
(4)準對角矩陣可逆的充分必要條件是:每個Ai(i=1,2,…,l)都可逆
![](/img/b/a4a/wZ2NnLjVWZlFmYzEmYlZzNxMGNmVmYyImNykTYzQzYlVWMzQ2LhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
![](/img/e/a69/wZ2NnL1MzYzkTZ5YGN1czMhFWOlRDNjFjMyMGZlNjMzcTOyQzLhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
(5)設A是準對戶狼漏角矩陣,則埋寒訂淚連危判|A|=|A1||A2|…|Al|