Dense Matrices

Matrix Class Reference

class sympy.matrices.dense.MutableDenseMatrix

col_del(i)

Delete the given column.

Examples

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

See also

col, row_del

col_op(j, f)

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

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]])

See also

col, row_op

col_swap(i, j)

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

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]])

See also

col, row_swap

copyin_list(key, value)

Copy in elements from a list.

Parameters

key : slice

The section of this matrix to replace.

value : iterable

The iterable to copy values from.

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]])

See also

copyin_matrix

copyin_matrix(key, value)

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.

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]])

See also

copyin_list

fill(value)

Fill the matrix with the scalar value.

See also

zeros, ones

row_del(i)

Delete the given row.

Examples

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

See also

row, col_del

row_op(i, f)

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

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]])

See also

row, zip_row_op, col_op

row_swap(i, j)

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

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]])

See also

row, col_swap

simplify(ratio=1.7, measure=<function count_ops>, rational=False, inverse=False)

Applies simplify to the elements of a matrix in place.

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

See also

sympy.simplify.simplify.simplify

zip_row_op(i, k, f)

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

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]])

See also

row, row_op, col_op

ImmutableMatrix Class Reference

class sympy.matrices.immutable.ImmutableDenseMatrix

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

is_diagonalizable(reals_only=False, **kwargs)

Returns true if a matrix is diagonalizable.

Parameters

reals_only : bool. If reals_only=True, determine whether the matrix can be

diagonalized without complex numbers. (Default: False)

Kwargs

clear_cachebool. If True, clear the result of any computations when finished.

(Default: True)

Examples

>>> from sympy import Matrix
>>> m = Matrix(3, 3, [1, 2, 0, 0, 3, 0, 2, -4, 2])
>>> m
Matrix([
[1,  2, 0],
[0,  3, 0],
[2, -4, 2]])
>>> m.is_diagonalizable()
True
>>> m = Matrix(2, 2, [0, 1, 0, 0])
>>> m
Matrix([
[0, 1],
[0, 0]])
>>> m.is_diagonalizable()
False
>>> m = Matrix(2, 2, [0, 1, -1, 0])
>>> m
Matrix([
[ 0, 1],
[-1, 0]])
>>> m.is_diagonalizable()
True
>>> m.is_diagonalizable(reals_only=True)
False

See also

is_diagonal, diagonalize

is_zero

Checks if a matrix is a zero matrix.

A matrix is zero if every element is zero. A matrix need not be square to be considered zero. The empty matrix is zero by the principle of vacuous truth. For a matrix that may or may not be zero (e.g. contains a symbol), this will be None

Examples

>>> from sympy import Matrix, zeros
>>> from sympy.abc import x
>>> a = Matrix([[0, 0], [0, 0]])
>>> b = zeros(3, 4)
>>> c = Matrix([[0, 1], [0, 0]])
>>> d = Matrix([])
>>> e = Matrix([[x, 0], [0, 0]])
>>> a.is_zero
True
>>> b.is_zero
True
>>> c.is_zero
False
>>> d.is_zero
True
>>> e.is_zero