Matrix Calculus

A₁ a₂ absolute adjugate AITKEN approximation arbitrary b₁ C₁ calculation characteristic equation coefficients complex component computed convergence corresponding D₁ deflation determinant diagonal elements diagonal matrix dominant eigenvalue dominant root e-values e₁ eigen eigencolumn eigenrows eigenvectors eliminated equal error factor follows further Gauss gonal Hermitian Hermitian matrix higher elementary divisors holds i-th ill-conditioned inserted inverse iterated vectors iteration method j-th k-th linear combination m₁ multiplications null matrix obtained orthogonal matrix orthogonal transformation P₁ plane polynomial principal vectors procedure proof Q₁ quadratic quadratic form quadric quotient R₁ rank relation replaced requires resp right side row and column S₁ scalar scalar product sequence Similarly simple product solution square starting vector symmetrical matrix system Ax t₁ theorem triangular matrix triangular system u₁ unknown V₁ values vanish W₁ x'Ax x₁ y₁ yields zero λ₁ λι ΣΣ