Class PositiveDefiniteness

java.lang.Object

org.flag4j.linalg.PositiveDefiniteness

public final class PositiveDefiniteness
extends Object

This class contains several methods for determining the positive definiteness of a matrix.

Method Summary

Modifier and Type	Method	Description
static boolean	isHermPosDef(CMatrix src)	Checks if the matrix is symmetric positive definite.
static boolean	isHermPosDef(Matrix src)	Checks if the matrix is symmetric positive definite.
static boolean	isPosDef(CMatrix src)	Checks if the matrix is positive definite.
static boolean	isPosDef(Matrix src)	Checks if the matrix is positive definite.
static boolean	isPosSemiDef(CMatrix src)	Checks if the matrix is positive semi-definite.
static boolean	isPosSemiDef(Matrix src)	Checks if the matrix is positive semi-definite.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

isPosDef

public static boolean isPosDef(Matrix src)

Checks if the matrix is positive definite. A matrix M is positive definite iff x^TMx > 0 for any vector x, or equivalently, if all eigenvalues are strictly greater than zero.

Parameters:

src - Matrix to check if it is positive definite.

Returns:

true if the matrix is positive definite; false otherwise.

See Also:

• isPosSemiDef(Matrix)

isPosDef

public static boolean isPosDef(CMatrix src)

Checks if the matrix is positive definite. A matrix M is positive definite iff x^TMx > 0 for any vector x, or equivalently, if the matrix is Hermitian and all eigenvalues are strictly greater than zero.

Parameters:

src - Matrix to check if it is positive definite.

Returns:

true if the matrix is positive definite; false otherwise.

See Also:

• isPosSemiDef(CMatrix)

isHermPosDef

public static boolean isHermPosDef(Matrix src)

Checks if the matrix is symmetric positive definite. A matrix M is positive definite iff x^TMx > 0 for any vector x, or equivalently, if all eigenvalues are strictly greater than zero.

Parameters:

src - Matrix to check if it is positive definite.

Returns:

true if the matrix is positive definite; false otherwise.

See Also:

• isPosSemiDef(Matrix)

isHermPosDef

public static boolean isHermPosDef(CMatrix src)

Checks if the matrix is symmetric positive definite. A matrix M is positive definite iff x^TMx > 0 for any vector x, or equivalently, if all eigenvalues are strictly greater than zero.

Parameters:

src - Matrix to check if it is positive definite.

Returns:

true if the matrix is positive definite; false otherwise.

See Also:

• isPosSemiDef(Matrix)

isPosSemiDef

public static boolean isPosSemiDef(Matrix src)

Checks if the matrix is positive semi-definite. A matrix M is positive semi-definite iff x^TMx >= 0 for any vector x, or equivalently, if the matrix is symmetric and all eigenvalues are greater than or equal to zero.

Parameters:

src - Matrix to check if it is positive semi-definite.

Returns:

true if the matrix is positive semi-definite; false otherwise.

See Also:

• isPosSemiDef(Matrix)

isPosSemiDef

public static boolean isPosSemiDef(CMatrix src)

Checks if the matrix is positive semi-definite. A matrix M is positive semi-definite iff x^TMx >= 0 for any vector x, or equivalently, if the matrix is Hermitian and all eigenvalues are greater than or equal to zero.

Parameters:

src - Matrix to check if it is positive semi-definite.

Returns:

true if the matrix is positive semi-definite; false otherwise.

See Also:

• isPosSemiDef(CMatrix)