線性代數(shù)-矩陣-教學(xué)ppt-資料下載頁
2025-08-07 10:51本頁面
【正文】 11jssijijiij abababd ???? ?2211jic ijd= 也就是 TTT ABAB ?)(TTTT ABCA B C ?)( ?11?????????????TnnTaa??jic ijd= 對(duì)稱陣與反對(duì)稱陣 AA T ?:對(duì)稱陣 AA T ??:反對(duì)稱陣TTT AAAAAA ?,TAA ?22TT AAAAA ????任一方陣都可以分解成 對(duì)稱陣與反對(duì)稱陣的和 . jiij aa ?0??? iijiij aaa 且例 1:設(shè)矩陣 A與 B為同階對(duì)稱陣，證明 AB是對(duì)稱 陣的充要條件為 AB=BA. 證： :? TAB )(? AB?TTT ABAB ?)(又 BA?BAAB ?????:? BAAB ??TTT ABAB ?? )( BA? AB?為對(duì)稱陣。AB?例 2：求矩陣的冪 ???????? ??????c oss i ns i nc osA??nA????????????????????2222s i nc osc oss i n2c oss i n2s i nc os???????? ??????2c os2s i n2s i n2c os???????? ????????? ??????????c oss i ns i nc osc oss i ns i nc os2A???????????????????)1c os ()1s i n()1s i n()1c os (1nnnnA n設(shè)???????? ?????????????????????????c o ss i ns i nc o s)1c o s ()1s i n ()1s i n ()1c o s (1nnnnAAAnn則???????? ??????nnnnc oss i ns i nc os???????? ???????nnnnA nc oss i ns i nc o
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