Zero determinant means columns and rows are linearly dependent vectors. Zero determinant means matrix is not invertible. Zero determinant means parallelepiped volumes are zero. Zero determinant means system of equations has non-trivial solution. Zero determinant means determinant of linear transformation is zero
Determinant is a scalar value from matrix operations. Can be denoted in three ways: determinant, determinant of matrix, determinant of matrix element
A non-singular matrix is a square matrix with a non-zero determinant. Determinant calculation is possible only for square matrices. Non-singular matrices are invertible and have a unique inverse
Minor is determinant of smaller matrix formed by removing rows and columns. First minor (i,j) is determinant of matrix with row i and column j removed. Zero-order minor is always 1. Total number of minors of size k is k × k
Lower triangular matrices have zeros above main diagonal. Upper triangular matrices have zeros below main diagonal. Lower triangular matrices denoted by L, upper triangular by U or R. Diagonal matrices are both upper and lower triangular
A 3x3 matrix contains 3 rows and 3 columns. A matrix is invertible if its determinant is non-zero. Every xxn square matrix has an inverse. The inverse of a matrix is represented by X