Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 12
... ( column ) x . The result is a 1 × 1 matrix zx given by n ZX = Στίχ i = 1 ( 1.37 ) In words the prescription becomes : To multiply the row z into the column x , multiply the leftmost element of z by the topmost element of x ; then ...
... ( column ) x . The result is a 1 × 1 matrix zx given by n ZX = Στίχ i = 1 ( 1.37 ) In words the prescription becomes : To multiply the row z into the column x , multiply the leftmost element of z by the topmost element of x ; then ...
Página 25
... column u as a linear combination of the eigenvectors of A suffices to enable the evaluation of f ( A ) and the solution of the initial value problems earlier considered . It will now be shown that an arbitrary column u may be written as ...
... column u as a linear combination of the eigenvectors of A suffices to enable the evaluation of f ( A ) and the solution of the initial value problems earlier considered . It will now be shown that an arbitrary column u may be written as ...
Página 248
... column y for the kth column of IM . The reader will note the equivalence of this with the solution previously given for two equations in two unknowns . To demonstrate the uniqueness of the solution , we suppose that x + , is another ...
... column y for the kth column of IM . The reader will note the equivalence of this with the solution previously given for two equations in two unknowns . To demonstrate the uniqueness of the solution , we suppose that x + , is another ...
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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Términos y frases comunes
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