Linear algebra of matrix

1. Definition of a matrix

1. Matrix is ​​a number of tables, unlike determinant rows and columns that must be equal, the number of rows and columns of the matrix is ​​not required. An equal number of rows and columns of the matrix is ​​called square.
2. Determinant is a numerical table operation, that is to say comprises an operational determinant. While the matrix is ​​only a number of tables, the table does not include the number of operations

2. Matrix operations

1. Addition and subtraction matrix. Addition and subtraction matrix must be the same type of matrix, a subtraction process for each subtraction corresponding to the matrix phase. Determinant of the number of addition and subtraction is addition and subtraction, as a determinant is a number

2. Matrix multiplication. Multiplied by columns of the matrix A is equal to B and A required number of rows of B. A process for the first column corresponds to each element and B obtained by multiplying the first row of the first row and first column of elements, each element corresponding to the second column of the first row of the A and B obtained by multiplying a first row, second column element ...

3. And the number of matrix multiplication. Each element of the matrix is ​​multiplied by this number. Multiplied by the number of determinant determinant determinant corresponding to a row or a column is multiplied by all elements of the number.

4. Matrix Binary Operations:

    	A+B=B+A
    	(A+B)+C=A+(B+C)
    	k(A+B)=kiA+kB
    	一般来讲AB不等于BA
    	AB=BC是不一定有A=C即矩阵不满足消去律
    	两个非零矩阵的乘积可以是零矩阵，行列式中不可能
    	C(A+B)=CA+CB
    	(AB)C=A(BC)
    	k(AB)=(kA)B
   

5. Matrix transpose, transpose the ranks of exchange is

    A的转置的转置等于A
    A+B的转置等于A的转置加上B的转置
    AB的转置等于B的转置乘以A的转置，位置发生了变化
    A方阵乘以B方阵的行列式等于A的行列式乘以B的行列式
   

3. inverse matrix

1. Inverse matrix is ​​AB = E, E is the identity matrix
2. If AB = E ,, then A, B are inverse matrix; if the determinant of matrix A so site 0, A is a square invertible
3. Adjoint matrix