Diagonal matrix

A matrix is a diagonal matrix if and only if all of its non-zero values exist along the diagonal.

• Each non-zero column of a diagonal matrix corresponds to a linearly independent basis vector.
• The values along the diagonal are eigenvalues of the matrix.
• The determinant of a diagonal matrix is the product of its diagonal terms.
  • Which implies that any diagonal matrix with at least one zero on the diagonal is singular.
• Every real-valued diagonal matrix is symmetric.