Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 11
... matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right . The product is then defined by ( mp ) is = Σ mikPkj k ( mx ) ; = Σm¡¡xj ( 1.29 ) As the reader will ...
... matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right . The product is then defined by ( mp ) is = Σ mikPkj k ( mx ) ; = Σm¡¡xj ( 1.29 ) As the reader will ...
Página 20
... matrix A commutes with another matrix B , then A commutes with any matrix of the form F ( B ) = Σ c „ B " where n is a positive integer and the c , are numbers . 12. Show that if A is any square matrix and I is the unit matrix , then IA ...
... matrix A commutes with another matrix B , then A commutes with any matrix of the form F ( B ) = Σ c „ B " where n is a positive integer and the c , are numbers . 12. Show that if A is any square matrix and I is the unit matrix , then IA ...
Página 64
... matrix . Any matrix H which satisfies the condition H H + is called a Hermitian matrix . Clearly , Hermitian matrices are normal matrices . Furthermore , any real symmetric matrix is a normal matrix , since such a matrix can be ...
... matrix . Any matrix H which satisfies the condition H H + is called a Hermitian matrix . Clearly , Hermitian matrices are normal matrices . Furthermore , any real symmetric matrix is a normal matrix , since such a matrix can be ...
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