[理學(xué)]線性代數(shù)ii-chapter-文庫吧資料
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【正文】 ????AAaAaAnmijnmij????(3) Addition of Matrices ? ? ? ?? ?? ?jibaccBAnmbBaAijijijnmijnmijnmij,p a i r e a c h f o r w h e r eT h e n m a t r i c e s . be a n d L e t ??????????Matrix addition is both mutative and associative, that is, ? ? ? ? ? ? ? ?? ? ? ? ? ? 0 。 1100101012101321 a n d ,110012030210bu t ???????????????????????(i) A matrix is in reduced row echelon form if (1). It is in row echelon form。...00...0...m a t r i x n g u l a r u p p e r t r i aA n 22211211?????????????nnnnaaaaaaA????。)0(m a t r ix z e r oA a nm ??O? ?? ?? ? ? ?? ? m a t r i x t h eof di a g on a lm a i n or t h edi a g on a l t h ec a l l e d ise n t r y ,e n t r y , 2,2 e n t r y ,1,1 t h ej oi n i n g l i n e t h e n t h e,m a t r i x a n is Ifm a t r i x a of D i a g on a l nnnnAb??)。 Inverse matrices and partitioned matrices 1. The Definition of Matrices This section will consider matrices and their operations. We will define algebraic operations such as addition, subtraction, and multiplication of matrices. Definition 1 m a t r i x . a n c a l l e d is c o l u m n s a n d r o w s i n s y m b o l s )( o r n u m b e r s ofa r r a y A n nmnm?or ),(s i m p l y o r , )(n o t a t i o n T h e ijnmij aAaA ?? ?167。 Determinants 167。Prof Liubiyu Matrix (matrices) 矩陣 A column vector 行向量 A square matrix 方陣 A row vector 列向量 A diagonal matrix 對角陣 An identity matrix 單位陣 An upper triangular matrix 上三角陣 A lower triangular matrix 下三角陣 A symmetric matrix 對稱陣 A skewsymmetric matrix 反對稱陣 Rowechelon form 行 階梯型 New Words array 排列 column 列 algebraic operations 代數(shù)運算 row 行 addition 加法 subtraction 減法 multiplication 乘法 entry 表值 ,元素 the transpose of a matrix 矩陣的轉(zhuǎn)置 mutative 可交換的 associative 可結(jié)合的 distributive 可分配的 New Words Linear algebra is a branch of mathematics dealing with matrices and vector spaces. Matrices have been introduced here as a handy tool for solving systems of linear equations, determining linear dependence of vectors and solving the problem of eigenvalue and eigenvector. They have also many applications in the other fields, such as statistics, economics, engineering, physics, chemistry, biology and business. Contents 167。 Matrices and matrix operations 167。 Cramer rule 167。 Matrices and matrix operations 1 1 1 2 12 1 2 2 212......o r . . . . . . . . . . . ....r e p r e s e n ts a n m a tr ix .nnm m m na a aa a aAa a am n A??????????????? ? e n t r y . , t h ec a l l e d isc ol u m n t h a n d r owth t h eofo n i n t e r s e c t i a t t h e a pp e a r s e n t r y t h a t T h ejiji? ?? ?nmijijaAjia??m a t r i x ofe n t r y , t h ede n ot e s s y m bol
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