Determináns
Determináns (determinant) is a scalar attribute of a square matrix. For an n×n matrix A over a field, det(A) is denoted det(A) or |A| and is zero exactly when A is singular. Geometrically, det(A) gives the factor by which A scales n-dimensional volumes under the associated linear transformation; its absolute value is the volume scale, while the sign indicates orientation preservation or reversal.
Computation: For a 2×2 matrix A = [[a, b], [c, d]], det(A) = ad − bc. For larger matrices,
Properties and applications: det(AB) = det(A) det(B). det(A^T) = det(A). det(kA) = k^n det(A) for an n×n matrix. If