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PARTI MATRIX CALCULUS
Measures of the Magnitude of a Matrix
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applied arbitrary Bodewig calculation characteristic equation CM CM coefficients component computed condensation convergence corresponding definite deflation derived system determinant diagonal elements diagonal matrix diagonal term dominant eigenvalue dominant root eigen eigencolumns eigenrows eigenvalues and vectors eigenvectors elementary divisors eliminated equal error exact factor follows formula Frobenius Further Gauss holds ill-conditioned inserted inverse iterated vectors iteration methods Jacobi known likewise linear combination linearly linearly independent MATRIX CALCULUS matrix of order multiplications null matrix number of operations obtained orthogonal transformation plane premultiplied procedure proof punched cards quadratic form quadric quotient reciprocal relation replaced requires resp right sides row and column scalar product Seidel sequence Similarly simple product solution square matrix starting vector subtracting sum of squares sum-column sum-row symmetrical matrix system Ax Theorem triangular matrix triangular system unit circle unknown vanish vm+1 vm+2 x'Ax yields zero