A matrix minor is the determinant of a square submatrix obtained by selecting rows and columns of a matrix. Over a field, the matrix rank is less than exactly when every -by- matrix minor vanishes. In a matrix of regular functions, these equations define a closed rank-defect locus, explaining the determinantal variety construction.
A principal minor is the determinant of a square submatrix selected using the same index set for rows and columns. For a three-by-three matrix, the coefficient of in its monic characteristic polynomial is the sum of its three principal minors of order two.
A leading principal minor is a principal minor using the first rows and columns of a square matrix in a specified ordering. Sylvester's criterion uses these minors to characterize positive-definite matrices.
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In linear algebra, a **minor** is a specific determinant that is associated with a square matrix. The minor of an element in a matrix is defined as the determinant of the submatrix formed by deleting the row and column in which that element is located.