rotation matrices
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21—30 of 70 matching pages
21: 35.4 Partitions and Zonal Polynomials
22: 22.6 Elementary Identities
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§22.6(iv) Rotation of Argument (Jacobi’s Imaginary Transformation)
…23: Bibliography T
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Rotating black holes: Separable wave equations for gravitational and electromagnetic perturbations.
Phys. Rev. Lett. 29 (16), pp. 1114–1118.
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Angular Momentum: An Illustrated Guide to Rotational Symmetries for Physical Systems.
A Wiley-Interscience Publication, John Wiley & Sons Inc., New York.
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24: 1.3 Determinants, Linear Operators, and Spectral Expansions
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Determinants of Upper/Lower Triangular and Diagonal Matrices
… ►§1.3(iv) Matrices as Linear Operators
… ►Real symmetric () and Hermitian () matrices are self-adjoint operators on . … ►For Hermitian matrices is unitary, and for real symmetric matrices is an orthogonal transformation. …25: 35.6 Confluent Hypergeometric Functions of Matrix Argument
26: 19.31 Probability Distributions
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►More generally, let () and () be real positive-definite matrices with rows and columns, and let be the eigenvalues of .
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27: 28.34 Methods of Computation
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(d)
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28: 23.22 Methods of Computation
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(b)
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(c)
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If , then
23.22.2
There are 4 possible pairs (, ), corresponding to the 4 rotations of a square lattice. The lemniscatic case occurs when and .
If , then
23.22.3
There are 6 possible pairs (, ), corresponding to the 6 rotations of a lattice of equilateral triangles. The equianharmonic case occurs when and .
29: 35.8 Generalized Hypergeometric Functions of Matrix Argument
30: Bibliography F
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Application of the -function theory of Painlevé equations to random matrices: PIV, PII and the GUE.
Comm. Math. Phys. 219 (2), pp. 357–398.
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Application of the -function theory of Painlevé equations to random matrices: , , the LUE, JUE, and CUE.
Comm. Pure Appl. Math. 55 (6), pp. 679–727.
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Application of the -function theory of Painlevé equations to random matrices: , the JUE, CyUE, cJUE and scaled limits.
Nagoya Math. J. 174, pp. 29–114.
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