Author(s): Kaare Brandt Petersen, Michael Syskind Pedersen
Edition: November 15, 2012
Year: 2012
Language: English
Pages: 72
Determinant......Page 6
The Special Case 2x2......Page 7
Derivatives of a Determinant......Page 8
Derivatives of an Inverse......Page 9
Derivatives of Matrices, Vectors and Scalar Forms......Page 10
Derivatives of Traces......Page 12
Derivatives of Structured Matrices......Page 14
Basic......Page 17
Exact Relations......Page 18
Approximations......Page 20
Pseudo Inverse......Page 21
Complex Derivatives......Page 24
Higher order and non-linear derivatives......Page 26
Inverse of complex sum......Page 27
Solutions to linear equations......Page 28
Eigenvalues and Eigenvectors......Page 30
Singular Value Decomposition......Page 31
LU decomposition......Page 32
LDL decompositions......Page 33
Definition of Moments......Page 34
Expectation of Linear Combinations......Page 35
Weighted Scalar Variable......Page 36
Student's t......Page 37
Wishart......Page 38
Wishart, Inverse......Page 39
Basics......Page 40
Moments......Page 42
Mixture of Gaussians......Page 44
Block matrices......Page 46
Discrete Fourier Transform Matrix, The......Page 47
Hermitian Matrices and skew-Hermitian......Page 48
Orthogonal matrices......Page 49
Positive Definite and Semi-definite Matrices......Page 50
Singleentry Matrix, The......Page 52
Toeplitz Matrices......Page 54
Transition matrices......Page 55
Units, Permutation and Shift......Page 56
Vandermonde Matrices......Page 57
Functions and Series......Page 58
Kronecker and Vec Operator......Page 59
Matrix Norms......Page 61
Integral Involving Dirac Delta Functions......Page 62
Miscellaneous......Page 63
Gaussian......Page 64
One Dimensional Mixture of Gaussians......Page 65
Misc Proofs......Page 66
