Algebra: A Text-book of Determinants, Matrices, and Algebraic Forms

a₁ b₁ c₁ a₂ algebraic forms ax²+2hxy+by² b₂ c₂ bilinear form CHAPTER co-factor coefficients consider coordinates corresponding covariant d₁ definition determinant of order discriminant elements equal example expressed factor fundamental set given Hence Hermitian form HINT homogeneous integer k₁ k₂ kth column l₁ Laplace expansion latent roots latent vectors leading diagonal letters linear transformation linearly independent matrix of order minant minor of order modulus Moreover non-singular matrix non-singular transformation non-zero notation obtained orthogonal matrix orthogonal transformation polynomial positive-definite form proof Prove quadratic form rank real numbers real or complex reciprocal result row and sth rows and columns rth row satisfy singular matrix skew-symmetric matrix skew-symmetrical determinant solution square matrix suffixes sum of multiples Theorem 11 Theorem 24 transpose unaltered unit matrix wherein write X₁ Y₁ Y₂ zero α₁ λ₁