Linear Algebra 4: Matrix

1.Matrix

A matrix is a set of vectors

If the matrix has m rows and n columns ,we say the size of the matrix is m by n,written m*n.

If m = n ,we call this matrix "square".We use M_{m*n}  to donote the set that cotains all matrices whose size is m*n.eg:M_{3*2}  has 3 rows and 2 columns.

2.The use of Matrix

2.1add and subtract

Two Matrixs with the same size(the number of rows and columns) can add and subtract(减).

2.2multiply

Matrix can multiply with a scalar.

2.3Zero Matrix(零矩阵) and Identity Matrix(单位矩阵)

(1)Zero Matrix:All elments are 0,which we donoted by O.

(2) Identity Matrix:It must be  square ,对角线是1，其他全是0.

2.4Properties

Properties

3.Transpose

 If A is an mxn matrix,A^T(transpose of A) is an nxm matrix whose (i,j)-entry is the (j-i)-entry of A.(行列互换)

3.1Properties

Properties
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