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The Minors of a Determinant
in The Product of Two Determinants
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adjacent interchanges algebraic form B'AB bilinear form called CHAPTER co-factors commutative law complex numbers consider Corollary corresponding covariant cross-ratio determinant of order discriminant elementary transformations elements equal expressed function fundamental set given Hence Hermitian form Hint homogeneous homogeneous coordinates integer ith row joint-invariant kth column Laplace expansion latent roots leading diagonal letters linear transformation matrix of order minant minor of order modulus Moreover non-singular matrix non-zero notation number of columns number of inversions obtained orthogonal matrix orthogonal transformation plane polynomial positive-definite form prefixed proof Prove quartic rank real numbers real or complex real quadratic form reciprocal rows and columns satisfied set of values singular matrix skew-symmetric matrix skew-symmetrical determinant square matrix suffixes sum of multiples summation convention Theorem 23 Theorem 39 total number transpose triangle of reference unit matrix variables xv wherein write written xv x2 zero