# Immutable Matrices¶

The standard Matrix class in Diofant is mutable. This is important for performance reasons but means that standard matrices can not interact well with the rest of Diofant. This is because the Basic object, from which most Diofant classes inherit, is immutable.

The mission of the ImmutableMatrix class is to bridge the tension between performance/mutability and safety/immutability. Immutable matrices can do almost everything that normal matrices can do but they inherit from Basic and can thus interact more naturally with the rest of Diofant. ImmutableMatrix also inherits from MatrixExpr, allowing it to interact freely with Diofant’s Matrix Expression module.

You can turn any Matrix-like object into an ImmutableMatrix by calling the constructor

>>> M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
>>> M[1, 1] = 0
>>> IM = ImmutableMatrix(M)
>>> IM
Matrix([
[1, 2, 3],
[4, 0, 6],
[7, 8, 9]])
>>> IM[1, 1] = 5
Traceback (most recent call last):
...
TypeError: Can not set values in Immutable Matrix. Use Matrix instead.


## ImmutableMatrix Class Reference¶

class diofant.matrices.immutable.ImmutableMatrix[source]

Create an immutable version of a matrix.

Examples

>>> 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

C

By-element conjugation.

adjoint()

Conjugate transpose or Hermitian conjugation.

as_mutable()

Returns a mutable version of this matrix

Examples

>>> 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]])

conjugate()

By-element conjugation.

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.

Examples

>>> 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

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

>>> 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