Added is_anti_hermitian.py

docs/refs.bib

@@ -1165,6 +1165,13 @@ @misc{WikiHerm
 
 }
 
+@misc{WikiAntiHerm,
+  author  = "Wikipedia",
+  title   = "Skew-Hermitian matrix",
+  howpublished = {https://en.wikipedia.org/wiki/Skew-Hermitian_matrix}
+
+}
+
 
 @misc{WikiHilbSchOp,
   author  = "Wikipedia",

toqito/matrix_props/__init__.py

@@ -3,6 +3,7 @@
 from toqito.matrix_props.has_same_dimension import has_same_dimension
 from toqito.matrix_props.is_square import is_square
 from toqito.matrix_props.kp_norm import kp_norm
+from toqito.matrix_props.is_anti_hermitian import is_anti_hermitian
 from toqito.matrix_props.is_hermitian import is_hermitian
 from toqito.matrix_props.is_positive_semidefinite import is_positive_semidefinite
 from toqito.matrix_props.is_density import is_density

toqito/matrix_props/is_anti_hermitian.py

@@ -0,0 +1,67 @@
+"""Is matrix an anti-Hermitian matrix."""
+
+import numpy as np
+
+from toqito.matrix_props.is_hermitian import is_hermitian
+
+
+def is_anti_hermitian(mat: np.ndarray, rtol: float = 1e-05, atol: float = 1e-08) -> bool:
+    r"""Check if matrix is anti-Hermitian (a.k.a. skew-Hermitian) :cite:`WikiAntiHerm`.
+
+    An anti-Hermitian matrix is a complex square matrix that is equal to the negative of its own
+    conjugate transpose.
+
+    Examples
+    ==========
+
+    Consider the following matrix:
+
+    .. math::
+        A = \begin{pmatrix}
+                2j & -1 + 2j & 4j \\
+                1 + 2j & 3j & -1 \\
+                4j & 1 & 1j
+            \end{pmatrix}
+
+    our function indicates that this is indeed an anti-Hermitian matrix as it holds that
+
+    .. math::
+        A = -A^*.
+
+    >>> from toqito.matrix_props import is_anti_hermitian
+    >>> import numpy as np
+    >>> mat = np.array([[2j, -1 + 2j, 4j], [1 + 2j, 3j, -1], [4j, 1, 1j]])
+    >>> is_anti_hermitian(mat)
+    True
+
+    Alternatively, the following example matrix :math:`B` defined as
+
+    .. math::
+        B = \begin{pmatrix}
+                1 & 2 & 3 \\
+                4 & 5 & 6 \\
+                7 & 8 & 9
+            \end{pmatrix}
+
+    is not anti-Hermitian.
+
+    >>> from toqito.matrix_props import is_anti_hermitian
+    >>> import numpy as np
+    >>> mat = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    >>> is_anti_hermitian(mat)
+    False
+
+    References
+    ==========
+    .. bibliography::
+        :filter: docname in docnames
+
+
+
+    :param mat: Matrix to check.
+    :param rtol: The relative tolerance parameter (default 1e-05).
+    :param atol: The absolute tolerance parameter (default 1e-08).
+    :return: Return True if matrix is anti-Hermitian, and False otherwise.
+
+    """
+    return is_hermitian(mat * 1j, rtol, atol)

toqito/matrix_props/tests/test_is_anti_hermitian.py

@@ -0,0 +1,23 @@
+"""Test is_hermitian."""
+
+import numpy as np
+
+from toqito.matrix_props import is_anti_hermitian
+
+
+def test_is_hermitian():
+    """Test if matrix is Hermitian."""
+    mat = np.array([[2j, -1 + 2j, 4j], [1 + 2j, 3j, -1], [4j, 1, 1j]])
+    np.testing.assert_equal(is_anti_hermitian(mat), True)
+
+
+def test_is_non_hermitian():
+    """Test non-Hermitian matrix."""
+    mat = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    np.testing.assert_equal(is_anti_hermitian(mat), False)
+
+
+def test_is_hermitian_not_square():
+    """Input must be a square matrix."""
+    mat = np.array([[-1, 1, 1], [1, 2, 3]])
+    np.testing.assert_equal(is_anti_hermitian(mat), False)