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 | \ m / = | p | | m | = | I | = 1 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 | \ m / = | p | | m | = | I | = 1 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 : Xx = - ŹM Σ Mix 2 max k = 1 , 2 , ... , r 1 = 1 | M ' | x = 7 + 1 ( 1A.12 ) where M ' is the rth order determinant of the coefficients on the left of ( 1A.10 ) and M is the cofactor of m1 in the determinant ...
... unique solution , namely : Xx = - ŹM Σ Mix 2 max k = 1 , 2 , ... , r 1 = 1 | M ' | x = 7 + 1 ( 1A.12 ) where M ' is the rth order determinant of the coefficients on the left of ( 1A.10 ) and M is the cofactor of m1 in the determinant ...
Contenido
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх