Linear algebra MOC

Matrix determinant

The determinant of a matrix is a scalar quantity uniquely defined by its properties, namely: linalg

1. , where is the identity matrix;
2. The exchange of two rows of multiplies the determinant by ;
3. Multiplying a row by a scalar multiplies the determinant by that scalar;
4. Adding any multiple of a different row to a given row does not affect the determinant.

Leibniz formula

The determinant of a matrix is given by linalg

which is known as the Leibniz formula for the determinant.

Proof

proof

See also

• Vandermonde determinant

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