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addition and scalar algebra Algorithm arbitrary augmented matrix basis vectors block matrix called change-of-basis matrix Chapter characteristic polynomial A(f column vector Consider the vector corresponding defined denoted det(A determinants of order diagonal blocks diagonalizable dimension dimW direct sum echelon form echelon matrix eigenvalue eigenvectors elementary row operations equal Example following theorem form a basis free variable Gaussian elimination given vectors homogeneous system identity matrix inner product space inverse leading unknown Let F linear combination linear equations linear mapping linear operator linearly independent mapping F matrix of coefficients matrix representation minimal polynomial n-square nomial nonzero entry nonzero rows nonzero vector notation obtain one-to-one orthonormal permutation pivot Pn(t properties Replace row canonical form row reduce row space scalar multiplication solve spanning set square matrix Step subset subspace Suppose symmetric system AX system of linear tion tr(A triangular matrix trix unique solution vector space written yields zero vector
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Robert A Armstrong - 1999 - Journal of Plankton Research
J Schlienz, G Mahler - 1996 - Physics Letters A
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Mugino Saeki - 1997
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