Linear Algebra Tools

import cyxwiz.linalg as la

# Matrix multiplication
C = la.matmul(A, B)
C = A @ B  # Operator overload

# Transpose
At = la.transpose(A)
At = A.T

# Inverse
A_inv = la.inv(A)

# Determinant
det = la.det(A)

# Trace
tr = la.trace(A)

# SVD (Singular Value Decomposition)
U, S, Vt = la.svd(A)
U, S, Vt = la.svd(A, full_matrices=False)  # Economy

# Eigendecomposition
eigenvalues, eigenvectors = la.eig(A)
eigenvalues = la.eigvals(A)  # Values only

# LU Decomposition
P, L, U = la.lu(A)

# QR Decomposition
Q, R = la.qr(A)

# Cholesky (for positive definite matrices)
L = la.cholesky(A)

# Direct solve (Ax = b)
x = la.solve(A, b)

# Least squares
x, residuals, rank, s = la.lstsq(A, b)

# Pseudo-inverse
A_pinv = la.pinv(A)
x = A_pinv @ b

# Norms
fro_norm = la.norm(A, 'fro')  # Frobenius
spectral_norm = la.norm(A, 2)  # Spectral
nuclear_norm = la.norm(A, 'nuc')  # Nuclear

# Properties
rank = la.matrix_rank(A)
cond = la.cond(A)  # Condition number