Basic Examples (3) 

Compute the sign and natural logarithm of the determinant of a matrix:

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The determinant:

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Or using the built-in function Det:

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Scope (6) 

Compute the sign and natural logarithm of the determinant of a real-valued matrix:

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Complex-valued array:

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A SparseArray object:

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A SymmetrizedArray object:

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Use a singular matrix:

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Use a large matrix:

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Compute the determinant:

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Properties and Relations (4) 

For real matrices, SignLogDet returns the signs as -1 or 1, depending on whether the determinant is negative or positive:

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The sign is zero if the determinant is 0:

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For complex matrices, the sign is a complex number with magnitude 1:

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Or complex zero for singular matrices:

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SignLogDet can give more accurate results than Det for small determinants:

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SignLogDet may give inaccurate results with machine-precision computation:

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Possible Issues (1) 

The logarithm value returned by SignLogDet may be too small to compute the determinant with machine precision:

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