Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 16
... unique inverse . Thus , suppose that there exist a pair of matrices p and m such that pm = I. Then , m is nonsingular ; as the following shows so that | pm | = | p | | m | = | I | = 1 [ m ] 0 Furthermore , it is clear that mx = my leads ...
... unique inverse . Thus , suppose that there exist a pair of matrices p and m such that pm = I. Then , m is nonsingular ; as the following shows so that | pm | = | p | | m | = | I | = 1 [ m ] 0 Furthermore , it is clear that mx = my leads ...
Página 17
... unique solution for each row of p follows from properties 1 and 2 taken in con- junction with the nonvanishing of the determinant of m . It has just been shown that p and q as required exist . To demonstrate their equality is trivial ...
... unique solution for each row of p follows from properties 1 and 2 taken in con- junction with the nonvanishing of the determinant of m . It has just been shown that p and q as required exist . To demonstrate their equality is trivial ...
Página 250
... unique solution , namely : Xk = -- Σ Μικ Σ Σ Mixxx i = 1 | M ' | x = 7 + 1 k = 1 , 2 , ... , r ( 1A.12 ) where M ' is the rth order determinant of the coefficients on the left of ( 1A.10 ) and M is the cofactor of mix in the determinant ...
... unique solution , namely : Xk = -- Σ Μικ Σ Σ Mixxx i = 1 | M ' | x = 7 + 1 k = 1 , 2 , ... , r ( 1A.12 ) where M ' is the rth order determinant of the coefficients on the left of ( 1A.10 ) and M is the cofactor of mix in the determinant ...
Contenido
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
Derechos de autor | |
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analytic approximate arbitrary asymptotic ax² Bessel function boundary conditions chap coefficients consider constant contour coordinates corresponding cylindrical functions d₁ d²/dx² defined denotes determinant diagonal differential equation Dirac notation ei(p eigen eigencolumn eigenfunctions eigenvalue equation eigenvalue problem eigenvector eikr element evaluate expansion finite number follows Fourier integral theorem function f(x given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral representation integrand inverse Laplacian linear lowest eigenvalue matrix method multiplication notation obtained operator orthonormality conditions perturbation plane relations result Ritz method row or column saddle point saddle-point method satisfy the orthonormality scattering sinh solution solve spherical spherical harmonics substitution transformation functions trial functions vanish variable vector vector space verified wave written yields zero ηπχ πρ ди ду дх