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
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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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