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 ZX n Σzixi 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 multiply ...
... ( column ) x . The result is a 1 × 1 matrix zx given by ZX n Σzixi 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 multiply ...
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 246
... column ) are zero , the value of the determinant is zero . Each term of the expansion of the determinant is zero , because each term contains one factor from the row ( or column ) of zeros . VI . If each element of any row ( or column ) ...
... column ) are zero , the value of the determinant is zero . Each term of the expansion of the determinant is zero , because each term contains one factor from the row ( or column ) of zeros . VI . If each element of any row ( or column ) ...
Contenido
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
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analytic approximate arbitrary asymptotic ax² Bessel function boundary conditions chap coefficients consider constant contour coordinates corresponding cylindrical functions d₁ d²/dx² defined denotes determinant diagonal differential equation Dirac notation ei(p eigen eigencolumn eigenfunctions eigenvalue equation eigenvalue problem eigenvector eikr element evaluate expansion finite number follows Fourier integral theorem function f(x given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral representation integrand inverse Laplacian linear lowest eigenvalue matrix method multiplication notation obtained operator orthonormality conditions perturbation plane relations result Ritz method row or column saddle point saddle-point method satisfy the orthonormality scattering sinh solution solve spherical spherical harmonics substitution transformation functions trial functions vanish variable vector vector space verified wave written yields zero ηπχ πρ ди ду дх