Matrix inversion (ii): Inverse matrix

1. Mathematical Definitions

　　Definition: for n-order matrix a, if there is an n-order matrix B, the

　　　　　　　　AB=BA=E

It is said that matrix a is reversible, and the matrix B is called a inverse matrix .

Theorem: If matrix A is reversible, then | A|≠0.

Theorem: If | a|≠0, the matrix A is reversible and

a-1=1/| a|*a*

2. Algorithm implementation

1) Determinant of matrix

    " " <summary>    " "returns the determinant of a matrix" " </summary>    " " <param name= "Dmatrix" >Original Matrix</param>    " " <returns></returns>    " " <remarks></remarks>     Public Shared FunctionDetofmatrix (ByValDmatrix asMatrix) asdeterminantDimTempdet as Newdeterminant (dmatrix.rowlength) fori =1  toTempdet.rank forj =1  toTempdet.rank Tempdet.item (i, J)=Dmatrix.item (i, J)Next        Next        ReturnTempdetEnd Function

2) matrix inversion

    " " <summary>    " "returns the inverse matrix of a matrix" " </summary>    " " <param name= "Imatrix" >Original Matrix</param>    " " <returns></returns>    " " <remarks></remarks>     Public Shared FunctionInversematrix (ByValImatrix asMatrix) asMatrixDimTempmatrix as NewMatrix (imatrix.rowlength, Imatrix.collength)DimTempdet asdeterminant =Matrix.detofmatrix (Imatrix)DimTempdetvalue as Double=Tempdet.value Tempmatrix=Matrix.adjointmatrix (Imatrix)MsgBox(Tempdetvalue)If  notTempdetvalue =0  Then            Return(Tempmatrix * (1/tempdetvalue)) Else            Return  Nothing        End If    End Function

Matrix inversion (ii): Inverse matrix