The Linear Algebra module provides comprehensive tools for performing matrix and vector computations in Nelson.
It includes functions for matrix factorization, decomposition, inversion, and analysis, as well as operations on eigenvalues, singular values, and subspaces.
The module supports advanced numerical methods for evaluating matrix properties, condition numbers, and transformations, enabling efficient and accurate solutions for a wide range of linear algebra problems.
-
balance
Diagonal scaling to improve eigenvalue accuracy.
-
bandwidth
Lower and upper matrix bandwidth.
-
chol
Cholesky factorization.
-
cond
Condition number for inversion.
-
condeig
Condition number with respect to eigenvalues.
-
det
Matrix determinant.
-
diff
Differences and approximate derivatives.
-
eig
Eigenvalues and eigenvectors.
-
expm
Computes the matrix exponential of a square matrix.
-
gradient
Numerical gradient.
-
inv
Matrix inverse.
-
isbanded
Determine if matrix is within specific bandwidth.
-
ishermitian
Computes if matrix is hermitian or skew-hermitian.
-
issymmetric
Computes if matrix is symmetric.
-
kron
Kronecker tensor product.
-
logm
Computes the matrix logarithm of a square matrix.
-
lu
LU matrix factorization.
-
orth
Range space of a matrix.
-
planerot
Givens plane rotation.
-
rank
Rank of matrix.
-
rcond
Inverse condition number.
-
rref
Gauss-Jordan elimination.
-
rsf2csf
Convert real Schur form to complex Schur form.
-
schur
Schur decomposition.
-
sqrtm
Computes the matrix square root of a square matrix.
-
subspace
Angle between two subspaces.
-
svd
Singular Value Decomposition.
-
trace
Matrix trace.
-
vecnorm
Vector-wise norm.
