Linear algebra MOC

Matrix determinant

The determinant of a matrix is a scalar quantity uniquely defined by its properties, namely: #m/def/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 #m/thm/linalg

which is known as the Leibniz formula for the determinant.

Proof

#missing/proof

See also

#state/develop | #lang/en | #SemBr