# `linalg` - library for linear algebra

## Table of contents

1. `addCol` - linear combination of matrix columns
2. `addRow` - linear combination of matrix rows
3. `adjoint` - Adjoint of a matrix
4. `angle` - The angle between two vectors
5. `basis` - basis for a vector space
6. `charmat` - characteristic matrix
7. `charpoly` - characteristic polynomial of a matrix
8. `col` - extract columns of a matrix
9. `companion` - Companion matrix of a univariate polynomial
10. `concatMatrix` - join matrices horizontally
11. `crossProduct` - cross product of three-dimensional vectors
12. `curl` - curl of a vector field
13. `delCol` - delete matrix columns
14. `delRow` - delete matrix rows
15. `det` - determinant of a matrix
16. `divergence` - divergence of a vector field
17. `eigenvalues` - eigenvalues of a matrix
18. `eigenvectors` - eigenvectors of a matrix
19. `expr2Matrix` - construct a matrix from equations
20. `factorCholesky` - the Cholesky decomposition of a matrix
21. `factorLU` - LU-decomposition of a matrix
22. `factorQR` - QR-decomposition of a matrix
23. `frobeniusForm` - Frobenius form of a matrix
24. `gaussElim` - Gaussian elimination
25. `gaussJordan` - Gauss-Jordan elimination
26. `grad` - vector gradient
27. `hermiteForm` - Hermite normal form of a matrix
28. `hessenberg` - Hessenberg matrix
29. `hessian` - Hessian matrix of a scalar function
30. `hilbert` - Hilbert matrix
31. `intBasis` - basis for the intersection of vector spaces
32. `inverseLU` - computing the inverse of a matrix using LU-decomposition
33. `invhilbert` - inverse of a Hilbert matrix
34. `isHermitean` - checks whether a matrix is Hermitean
35. `isPosDef` - test a matrix for positive definiteness
36. `isUnitary` - test whether a matrix is unitary
37. `jacobian` - Jacobian matrix of a vector function
38. `jordanForm` - Jordan normal form of a matrix
39. `matdim` - dimension of a matrix
40. `matlinsolve` - solving systems of linear equations
41. `matlinsolveLU` - solving the linear system given by an LU decomposition
42. `minpoly` - minimal polynomial of a matrix
43. `multCol` - multiply columns with a scalar
44. `multRow` - multiply rows with a scalar
45. `ncols` - number of columns of a matrix
46. `nonZeros` - number of non-zero elements of a matrix
47. `normalize` - normalize a vector
48. `nrows` - number of rows of a matrix
49. `nullspace` - basis for the null space of a matrix
50. `ogCoordTab` - table of orthogonal coordinate transformations
51. `orthog` - orthogonalization of vectors
52. `permanent` - permanent of a matrix
53. `pseudoInverse` - Moore-Penrose inverse of a matrix
54. `randomMatrix` - generate a random matrix
55. `rank` - rank of a matrix
56. `row` - extract rows of a matrix
57. `scalarProduct` - scalar product of vectors
58. `setCol` - change a column of a matrix
59. `setRow` - change a row of a matrix
60. `smithForm` - Smith canonical form of a matrix
61. `stackMatrix` - join matrices vertically
62. `submatrix` - extract a submatrix or a subvector from a matrix or a vector, respectively
63. `substitute` - replace a part of a matrix by another matrix
64. `sumBasis` - basis for the sum of vector spaces
65. `swapCol` - swap two columns in a matrix
66. `swapRow` - swap two rows in a matrix
67. `sylvester` - Sylvester matrix of two polynomials
68. `tr` - trace of a matrix
69. `transpose` - transpose of a matrix
70. `vandermondeSolve` - solve a linear Vandermonde system
71. `vecdim` - number of components of a vector
72. `VectorOf` - type specifier for vectors
73. `vectorPotential` - vector potential of a three-dimensional vector field
74. `wiedemann` - solving linear systems by Wiedemann's algorithm

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