Matrix Creationnormal Matrix | sp.Matrix([[1,2],[3,4]]) | Matrix with all zeros | sp.zeros(4,5) | Matrix with all ones | sp.ones(4,5) | Square matrix with all zeros | sp.zeros(5) | Square matrix with all ones | sp.ones(5) | Identity matrix | sp.eyes(5) | Diagonal Matrix | sp.diag(1,2,3,4) | Generate element with func(i,j) | sp.Matrix(2,3,func) |
Matrix ModificationDelete the i-th row | M.row_del(i) | Delete the j-th column | M.col_del(j) | Row join M1 and M2 | M1.row_join(M2) | Column join M1 and M2 | M1.col_join(M2) |
Indexing(Slicing)get the element in M at (i,j) | M[i,j] | get the i-th row in M | M.row(i) | get the i-th row in M | M[i,:] | get the j-th column in M | M.col(j) | get the j-th column in M | M[:,j] | get the i-th and the k-th rows | M[[i,k],:] | get the j-th and the k-th columns | M[:,[j,k]] | get rows from i to k | M[i:k,:] | get columns from j to k | M[:,j:k] | get sub-matrix (row i to k,col j to l) | M[i:k,j:l] |
Note: All indices start from 0 | | Basic opertaionsSum | A+B | Substraction | A-B | Matrix Multiply | A*B | Scalar Multiply | 5*A | Elementwise product | sp.matrix_multiply_elementwise(A,B) | Transpose | A.T | Determinant | A.det() | Inverse | A.inv() | Condition Number | A.condition_number() | Row count | A.rows | Column count | A.cols | Trace | A.trace() |
Elementary Row OperationsReplacement | m.row_op(i, lambda ele,col:ele+m.row(j)[col]*c) | Interchange | M.row_swap(i,j) | Scaling | m.row_op(i,lambda ele,col:ele*c) |
Linear EquationsEchelon From | M.echelon_form() | Reduced Echelon Form | M.rref() | Solve AX=B (B can be a matrix) | x,freevars=A.gauss_jordan_solve(B) | least-square fit Ax=b | A.solve_least_squares(b) | solve Ax=b | A.solve(b) |
Vector SpaceBasis of column space | M.columnspace() | Basis of null space | M.nullspace() | Basis of row space | M.rowspace() | Rank | M.rank() |
| | Eigenvalues amd EigenvectorsFind the eigenvalues | M.eigenvals() | Find the eignevalues and the corresponding eigenspace | M.eigenvects() | Diagonalize a matrix | P, D = M.diagonalize() | test if the matrix is diagonalizable | M.is_diagonalizable | Calculate Jordan From | P, J = M.jordan_form() |
DecompositionLU Decomposition(PA=LU) | P,L,U=A.LUdecomposition() | QR Decomposition | Q,R=A.QRdecomposition() |
Vector OperationsCreate a column vector | v=sp.Matrix([1,2,3]) | dot product | v1.dot(v2) | cross product | v1.cross(v2) | length of the vector | v.norm() | normalize of vector | v.normalize() | the projection of v1 on v2 | v1.project(v2) | Gram-Schmidt orthogonalize | sp.GramSchmidt([v1,v2,v3]) | Gram-Schmidt orthogonalize with normalization | sp.GramSchmidt([v1,v2,v3],True) | Singular values | M.singlular_values() |
Block MatrixCreate a matrix by block | M=sp.Matrix([[A,B],[C,D]]) |
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