第2章矩阵代æ•&

第2章矩阵代æ•&

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
2008 春季班 线性代数 第二章 矩阵代数 2 1 第2章 矩阵代数 2.1 矩阵的概念 mn 个数排成 列的数表 m n mn m m n n a a a a a a a a a " " " " " " " 2 1 2 22 21 1 12 11 称为矩阵,记作 A .其中 称作矩阵 ij a A 的第 i 行第 j 列的元素. 两个矩阵如果大小一样,就说他们是同型的. 两个同型的矩阵,如果对应的元素也都一样,就 说这两个矩阵相等. ,即 1 = m A n × 1 的, ( ) n a a a A , , , 2 1 " = 称为行矩阵或行向量;若 ,即 1 = n A 的, 1 × m = m a a a A # 2 1 称为列矩阵或 列向量;若 1 = = n m ,这是一个 1 1 × 的矩阵,只 有一个元素,就看成是一个数,按数的规律进行运算.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2008 春季班 线性代数 第二章 矩阵代数 2 2 2.2 矩阵的运算 两个同型的矩阵可以做加法,它们的和是和它们 同型的矩阵,相加的规则是矩阵中对应的元素相 加.即 ( ) n m ij a A × = ( ) n m ij b B × = ,则 ( ) n m ij ij b a B A × + = + 矩阵加法的运算性质: (1) 交换律 A B B A + = + (2) 结合律 C B A C B A + + = + + ) ( ) ( (3) 有零矩阵0,对任意矩阵 A ,有 A A A = + = + 0 0 (4) 任意矩阵 A ,都有负矩阵 A ,使得 0 ) ( = + A A 其中 ( ) ij a A = k 是一个数, ( ) n m ij a A × = ,则 数 k 和矩阵 A 的数乘为 ( ) n m ij ka kA × = l k , 是两个常数, B A , 是同型矩阵,则 (1) A A = 1 0 0 = A
Background image of page 2
春季班 线性代数 第二章 矩阵代数 2 3 (2) A kl lA k ) ( ) ( = (3) kB kA B A k + = + ) ( (4) lA kA A l k + = + ) ( ( ) l m ij a A × = ( ) n l ij b B × = ,则 ( ) n m ij c AB × = 其中 lj il j i j i ij b a b a b a c + + + = " 2 2 1 1 矩阵乘法有性质: (1)结合律 C AB BC A ) ( ) ( = (2)分配律 BC AC C B A + = + ) CB CA B A C + = + ) ( (3) k 是常数,则 ) ( ) ( ) ( kB A B kA AB k = = z B A , n 阶方阵,则 B A AB = 设矩阵 A n 阶方阵, A 可以自乘,
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/14/2011 for the course MATH Probabilit taught by Professor Sata during the Summer '08 term at Tianjin University.

Page1 / 14

第2章矩阵代æ•&

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online