gh-39758: Improve crosslink between matrix methods and small optimization
    
As in the title. Also fix a few typos.

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URL: #39758
Reported by: user202729
Reviewer(s): Travis Scrimshaw

Author: Release Manager

src/sage/matrix/matrix2.pyx

@@ -15697,6 +15697,10 @@ cdef class Matrix(Matrix1):
         Return the conjugate of self, i.e. the matrix whose entries are the
         conjugates of the entries of ``self``.
 
+        .. SEEALSO::
+
+            :attr:`C`
+
         EXAMPLES::
 
             sage: # needs sage.rings.complex_double sage.symbolic
@@ -15752,6 +15756,10 @@ cdef class Matrix(Matrix1):
             though there is substantial variation and some confusion with
             the use of that term.
 
+        .. SEEALSO::
+
+            :meth:`conjugate`, :meth:`~.Matrix_dense.transpose`, :attr:`H`
+
         OUTPUT:
 
         A matrix formed by taking the complex conjugate of every entry
@@ -18569,6 +18577,10 @@ cdef class Matrix(Matrix1):
         r"""
         Return the conjugate-transpose (Hermitian) matrix.
 
+        .. SEEALSO::
+
+            :meth:`conjugate_transpose`
+
         EXAMPLES::
 
             sage: A = matrix(QQbar, [[     -3,  5 - 3*I, 7 - 4*I],                      # needs sage.rings.number_field
@@ -18579,7 +18591,7 @@ cdef class Matrix(Matrix1):
             [ 5 + 3*I -1 - 6*I -3 - 6*I]
             [ 7 + 4*I  3 - 5*I  5 - 1*I]
         """
-        return self.conjugate().transpose()
+        return self.conjugate_transpose()
 
 
 def _smith_diag(d, transformation=True):

src/sage/matrix/matrix_dense.pyx

@@ -114,7 +114,7 @@ cdef class Matrix_dense(matrix.Matrix):
             [1 2]
             [3 4]
 
-        ``.T`` is a convenient shortcut for the transpose::
+        :attr:`~sage.matrix.matrix2.Matrix.T` is a convenient shortcut for the transpose::
 
            sage: A.T
            [1 3]

src/sage/matrix/matrix_double_dense.pyx

@@ -1881,7 +1881,7 @@ cdef class Matrix_double_dense(Matrix_numpy_dense):
 
         OUTPUT:
 
-        ``U, S, V`` -- immutable matrices such that ``A = U*S*V.conj().transpose()``
+        ``U, S, V`` -- immutable matrices such that ``A = U*S*V.conjugate_transpose()``
         where `U` and `V` are orthogonal and `S` is zero off of the diagonal
 
         Note that if ``self`` is m-by-n, then the dimensions of the