Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 14
... matrix m exists such that qm = I where I is the unit matrix . Thus , suppose that m exists . Then pqm = = p ( qm ) ... nonsingular matrices have the properties mentioned earlier in this section for nonzero numbers . Thus , the prod- uct of two ...
... matrix m exists such that qm = I where I is the unit matrix . Thus , suppose that m exists . Then pqm = = p ( qm ) ... nonsingular matrices have the properties mentioned earlier in this section for nonzero numbers . Thus , the prod- uct of two ...
Página 17
... matrix m has a unique inverse ( denoted m - 1 ) if and only if the determinant of m does not vanish . This inverse may be written explicitly in usable form for 2 × 2 and 3 x 3 nonsingular matrices . Let D denote the determinant of m ...
... matrix m has a unique inverse ( denoted m - 1 ) if and only if the determinant of m does not vanish . This inverse may be written explicitly in usable form for 2 × 2 and 3 x 3 nonsingular matrices . Let D denote the determinant of m ...
Página 18
... matrix may now be defined as the maximum number of linearly independent columns which the matrix has . A nonsingular matrix has rank n , since the nonvanishing of the determinant of m implies that the only solution of mx = 0 is x = 0 ...
... matrix may now be defined as the maximum number of linearly independent columns which the matrix has . A nonsingular matrix has rank n , since the nonvanishing of the determinant of m implies that the only solution of mx = 0 is x = 0 ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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Términos y frases comunes
approximate arbitrary ax² basis Bessel function boundary conditions chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined denoted determinant diagonal differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector eikr evaluate expansion finite number follows Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplace transform Laplacian linear operator linearly independent lowest eigenvalue matrix membrane method multiplication nonsingular normal obtained orthonormality conditions plane problem procedure relations representation result satisfies the boundary scattering sinh solve spherical spherical harmonics string Substitution theorem trial functions vanish variable vector space Verify wave write written y₁ yields York zero ηπχ πο ποχ ди ду дх