# CxCheckPosDef

Advanced Analysis Library Only

AnalysisLibErrType CxCheckPosDef (void *inputMatrix, int matrixSize, int *positiveDefinite);

## Purpose

Checks if the complex, square input matrix is positive definite. A complex, square matrix is positive definite if and only if it is symmetric and the quadratic form

xHAx > 0

is true for all nonzero vectors x. For more information about positive definite matrices, refer to Matrix Computations by G.H. Golub and C.F. VanLoan, cited in the Bibliography.

## Parameters

Input
Name | Type | Description
inputMatrix | numeric array | Contains the input matrix that is to be tested for positive definiteness. This matrix must be an array of ComplexNum. The following C typedef statement defines the ComplexNum structure: typedef struct { double real; double imaginary; } ComplexNum;
matrixSize | integer | Number of elements in one dimension of the matrix.
Output
Name | Type | Description
positiveDefinite | integer | 1 if the input matrix is positive definite; 0 otherwise.

## Return Value

Name | Type | Description
status | AnalysisLibErrType | A value that specifies the type of error that occurred. Refer to analysis.h for definitions of these constants.