# Dense Matrices¶

## Matrix Class Reference¶

class sympy.matrices.dense.MutableDenseMatrix[source]
col_del(i)[source]

Delete the given column.

See also

col, row_del

Examples

>>> from sympy.matrices import eye
>>> M = eye(3)
>>> M.col_del(1)
>>> M
Matrix([
[1, 0],
[0, 0],
[0, 1]])

col_op(j, f)[source]

In-place operation on col j using two-arg functor whose args are interpreted as (self[i, j], i).

See also

col, row_op

Examples

>>> from sympy.matrices import eye
>>> M = eye(3)
>>> M.col_op(1, lambda v, i: v + 2*M[i, 0]); M
Matrix([
[1, 2, 0],
[0, 1, 0],
[0, 0, 1]])

col_swap(i, j)[source]

Swap the two given columns of the matrix in-place.

See also

col, row_swap

Examples

>>> from sympy.matrices import Matrix
>>> M = Matrix([[1, 0], [1, 0]])
>>> M
Matrix([
[1, 0],
[1, 0]])
>>> M.col_swap(0, 1)
>>> M
Matrix([
[0, 1],
[0, 1]])

copyin_list(key, value)[source]

Copy in elements from a list.

Parameters : key : slice The section of this matrix to replace. value : iterable The iterable to copy values from.

See also

copyin_matrix

Examples

>>> from sympy.matrices import eye
>>> I = eye(3)
>>> I[:2, 0] = [1, 2] # col
>>> I
Matrix([
[1, 0, 0],
[2, 1, 0],
[0, 0, 1]])
>>> I[1, :2] = [[3, 4]]
>>> I
Matrix([
[1, 0, 0],
[3, 4, 0],
[0, 0, 1]])

copyin_matrix(key, value)[source]

Copy in values from a matrix into the given bounds.

Parameters : key : slice The section of this matrix to replace. value : Matrix The matrix to copy values from.

See also

copyin_list

Examples

>>> from sympy.matrices import Matrix, eye
>>> M = Matrix([[0, 1], [2, 3], [4, 5]])
>>> I = eye(3)
>>> I[:3, :2] = M
>>> I
Matrix([
[0, 1, 0],
[2, 3, 0],
[4, 5, 1]])
>>> I[0, 1] = M
>>> I
Matrix([
[0, 0, 1],
[2, 2, 3],
[4, 4, 5]])

fill(value)[source]

Fill the matrix with the scalar value.

See also

zeros, ones

row_del(i)[source]

Delete the given row.

See also

row, col_del

Examples

>>> from sympy.matrices import eye
>>> M = eye(3)
>>> M.row_del(1)
>>> M
Matrix([
[1, 0, 0],
[0, 0, 1]])

row_op(i, f)[source]

In-place operation on row i using two-arg functor whose args are interpreted as (self[i, j], j).

See also

row, zip_row_op, col_op

Examples

>>> from sympy.matrices import eye
>>> M = eye(3)
>>> M.row_op(1, lambda v, j: v + 2*M[0, j]); M
Matrix([
[1, 0, 0],
[2, 1, 0],
[0, 0, 1]])

row_swap(i, j)[source]

Swap the two given rows of the matrix in-place.

See also

row, col_swap

Examples

>>> from sympy.matrices import Matrix
>>> M = Matrix([[0, 1], [1, 0]])
>>> M
Matrix([
[0, 1],
[1, 0]])
>>> M.row_swap(0, 1)
>>> M
Matrix([
[1, 0],
[0, 1]])

simplify(ratio=1.7, measure=<function count_ops at 0xaa0de9c>)[source]

Applies simplify to the elements of a matrix in place.

This is a shortcut for M.applyfunc(lambda x: simplify(x, ratio, measure))

zip_row_op(i, k, f)[source]

In-place operation on row i using two-arg functor whose args are interpreted as (self[i, j], self[k, j]).

See also

row, row_op, col_op

Examples

>>> from sympy.matrices import eye
>>> M = eye(3)
>>> M.zip_row_op(1, 0, lambda v, u: v + 2*u); M
Matrix([
[1, 0, 0],
[2, 1, 0],
[0, 0, 1]])


## ImmutableMatrix Class Reference¶

class sympy.matrices.immutable.ImmutableMatrix[source]

Create an immutable version of a matrix.

Examples

>>> from sympy import eye
>>> from sympy.matrices import ImmutableMatrix
>>> ImmutableMatrix(eye(3))
Matrix([
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]])
>>> _[0, 0] = 42
Traceback (most recent call last):
...
TypeError: Cannot set values of ImmutableDenseMatrix

ImmutableMatrix.C

By-element conjugation.

ImmutableMatrix.adjoint()

Conjugate transpose or Hermitian conjugation.

ImmutableMatrix.as_mutable()

Returns a mutable version of this matrix

Examples

>>> from sympy import ImmutableMatrix
>>> X = ImmutableMatrix([[1, 2], [3, 4]])
>>> Y = X.as_mutable()
>>> Y[1, 1] = 5 # Can set values in Y
>>> Y
Matrix([
[1, 2],
[3, 5]])

ImmutableMatrix.equals(other, failing_expression=False)

Applies equals to corresponding elements of the matrices, trying to prove that the elements are equivalent, returning True if they are, False if any pair is not, and None (or the first failing expression if failing_expression is True) if it cannot be decided if the expressions are equivalent or not. This is, in general, an expensive operation.

See also

sympy.core.expr.equals

Examples

>>> from sympy.matrices import Matrix
>>> from sympy.abc import x
>>> from sympy import cos
>>> A = Matrix([x*(x - 1), 0])
>>> B = Matrix([x**2 - x, 0])
>>> A == B
False
>>> A.simplify() == B.simplify()
True
>>> A.equals(B)
True
>>> A.equals(2)
False


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