Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 10
... equal if each element of one equals the corresponding element of the other . Thus , if m and p are matrices and x and y are columns ( or rows ) , m p implies m¡¡ x = y implies x ; = = Pij all i and j all i Yi ( 1.26 ) To multiply a ...
... equal if each element of one equals the corresponding element of the other . Thus , if m and p are matrices and x and y are columns ( or rows ) , m p implies m¡¡ x = y implies x ; = = Pij all i and j all i Yi ( 1.26 ) To multiply a ...
Página 15
... equal to the determinant of the trans- pose of the matrix , where the transpose of a matrix m , written as m2 , is defined by ( m2 ) ;; = mji 2. The necessary and sufficient condition that n simultaneous linear algebraic equations in n ...
... equal to the determinant of the trans- pose of the matrix , where the transpose of a matrix m , written as m2 , is defined by ( m2 ) ;; = mji 2. The necessary and sufficient condition that n simultaneous linear algebraic equations in n ...
Página 194
... equal to n2 . It is equal to zero when μ = 2mm / n , where m is an integer and m / n is not . The relation - μ k ( n 。— n ) • b = 2mπ = m = = 0 , 1 , 2 , . . . ( 13.76 ) is the grating equation . If one makes the substitutions - no b ...
... equal to n2 . It is equal to zero when μ = 2mm / n , where m is an integer and m / n is not . The relation - μ k ( n 。— n ) • b = 2mπ = m = = 0 , 1 , 2 , . . . ( 13.76 ) is the grating equation . If one makes the substitutions - no b ...
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