# 2.2.3.9.44 matrixbase::Inverse

## Description

Replace this matrix with the Inverse of this matrix.

## Syntax

int Inverse( )

## Return

Returns 0 on success or one of the following error codes on failure:

-1 = Matrix is not N x N

366 = The matrix is singular, possibly due to rounding errors; or the underlying type of matrix is not double.

11 = N must not be less than 1.

73 = Memory allocation failed.

## Examples

EX1

// Compute an inverse matrix
void matrixbase_Inverse_ex1()
{
int rc;

matrix<double> mat1 = {
{2,  3},
{3,  4}
};
//   Inverse matrix is:
//      {-4,  3}
//      { 3, -2}

MatrixPage MatPg1;
MatPg1.Create("Origin");
MatrixLayer MatLy1 = MatPg1.Layers(0);
Matrix Mat1(MatLy1);
Mat1 = mat1;
printf("  Original matrix is %s.\n",Mat1.GetName());

MatrixPage MatPg2;
MatPg2.Create("Origin");
MatrixLayer MatLy2 = MatPg2.Layers(0);
Matrix Mat2(MatLy2);
Mat2 = mat1;

rc=Mat2.Inverse(); // Compute the inverse matrix
if(rc!=0)
printf("  Error: Inverse failed. Error Code=%d\n",rc);
else
printf("  Inverse matrix is %s.\n",Mat2.GetName());
}

EX2

#define MAKEMAT(X) MatrixLayer MatLy##X;MatLy##X.Create();Matrix Mat##X(MatLy##X)
void mDivideTest1_ex2()
{
matrix mat1 = {
{1, 2, 3},
{4, 5, 6},
{1, 1, 1}
};
matrix mat2 = {
{2, 3, 4},
{1, 1, 1},
{4, 5, 4}
};

MAKEMAT(1); MAKEMAT(2); MAKEMAT(3); MAKEMAT(4); MAKEMAT(5);
Mat1=mat1; Mat2=mat2;
matrix mat3;
mat3=mat2;

mat3.Inverse();
Mat3=mat1*mat3;  //= mat1*Inv(mat2)
printf("%s = %s*Inv(%s) <== proper division of 2 matrices\n",Mat3.GetName(),Mat1.GetName(),Mat2.GetName());

Mat4=mat1/10;
printf("%s = %s/10 <== scaler division of a matrix\n",Mat4.GetName(),Mat1.GetName(),Mat2.GetName());

Mat5=mat1;
Mat5.DotDivide(mat2);
printf("%s = DotDivide(%s,%s) <== element-wise division of 2 matrices\n",Mat5.GetName(),Mat1.GetName(),Mat2.GetName());
}

## Remark

Replace this matrix with the Inverse of this matrix. An error is returned if the underlying base type of the matrix is not double.

Note

The following is a summary of various matrix operations:

1) Multiplication:

1-1) * ... Proper multiplication of 2 matrices (mat1*mat2)

1-2) * ... Scaler multiplication of a matrix (mat1*A or A*mat1)

1-3) DotMultiply ... Element-wise multiplication of 2 matrices

1-4) Cross ... Cross product of 2 matrices

1-5) CumulativeProduct ... cumulative product of a matrix

2) Division:

2-1) / ... Not defined for 2 matrices. For proper division, multiply Inverse(mat1)

2-2) / ... Scaler division of a matrix (mat1/A)

2-3) DotDivide ... Element-wise division of 2 matrices

3-1) + ... Element-wise addition of 2 matrices

3-2) + ... Scaler addition of a matrix (mat1+A or A+mat1)

3-3) SumColumns ... Summation of each column in a matrix

3-4) CumulativeSum ... Cumulative product of a matrix

4) Subtraction:

4-1) - ... Element-wise subtraction of 2 matrices

4-2) - ... Scaler subtraction of a matrix (mat1-A or A-mat1)

4-3) Difference ... Difference of adjacent 2 rows in a matrix (1st order differential)

5) Power:

5-1) ^ (or pow) ... Not defined as element-wise power of 2 matrices

5-2) ^ (or pow) ... Not defined as scaler power of a matrix

5-3) DotPower ... Element-wise power of 2 matrices

To depict the differences of above divisions, try the EX2.