A Fourier Theorem for Matrices
A Fourier Theorem for Matrices
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In our eReader you can find the full English version of the book. Read A Fourier Theorem for Matrices Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A Fourier Theorem for Matrices
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3) idV - idH - -^r [idH, iH] + -jj I [idH, xH] iHj 7, . (see [l])* where, for any matrices A, B, (2, U) [a, 3] - AB - BA, r [a, b]bJ - AB^ - 2BAB + B^A, ... The matrix dV is heimitianj if we write (2. 5) dV » (dcr ) + i(da ) (v, n - l, ... , n) then the r? variables dCT^. (v < n) and da (v < ^x) become linear functions of the n variables ds, . , (v < p. ) and da. , . (v < ix)« -5- 2 The deteiroinant D of these n linear functions is the factor of TT d3 TT da in equation (leU) times another factor which is a power " V, M. " v, M- of i. We shall determine D by diagonalizing H, For this purpose we shall first apply the following preliminary consideration. Let w be any unitary matrix 2 of n rows and col-umns. Let S be the space of n real dimensions whose points H correspond to the hermitian matrices. We shall represent the points in this space by the variables X, - X, ,. (v < n), (2. 6; (v, M. « l, . ». , n) V =» -y (v < li), where x may stand for either s or d CT and y may stand for either we obtain a linear mapping of S upon itself by choosing an arbitrary unitary matrix W and putting (2.
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To quickly assess the difficulty of the text, read a short excerpt:
3) idV - idH - -^r [idH, iH] + -jj I [idH, xH] iHj 7, . (see [l])* where, for any matrices A, B, (2, U) [a, 3] - AB - BA, r [a, b]bJ - AB^ - 2BAB + B^A, ... The matrix dV is heimitianj if we write (2. 5) dV » (dcr ) + i(da ) (v, n - l, ... , n) then the r? variables dCT^. (v < n) and da (v < ^x) become linear functions of the n variables ds, . , (v < p. ) and da. , . (v < ix)« -5- 2 The deteiroinant D of these n linear functions is the factor of TT d3 TT da in equation (leU) times another factor which is a power " V, M. " v, M- of i. We shall determine D by diagonalizing H, For this purpose we shall first apply the following preliminary consideration. Let w be any unitary matrix 2 of n rows and col-umns. Let S be the space of n real dimensions whose points H correspond to the hermitian matrices. We shall represent the points in this space by the variables X, - X, ,. (v < n), (2. 6; (v, M. « l, . ». , n) V =» -y (v < li), where x may stand for either s or d CT and y may stand for either we obtain a linear mapping of S upon itself by choosing an arbitrary unitary matrix W and putting (2.
What to read after A Fourier Theorem for Matrices?
You can find similar books in the "Read Also" column, or choose other free books by W Magnus to read online
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