Section 6.4 Transpose and Conjugate
The transpose of a matrix is obtained by flipping it over its diagonal, swapping rows with columns. The transpose is denoted as \(A^T\) and can be computed in Sage using the
transpose method: A matrix \(A\) is symmetric if it is equal to its transpose, i.e., \(A = A^T\text{.}\) Sage offers
is_symmetric() method to check if a matrix is symmetric. For matrices with complex entries, the complex conjugate is found by taking the conjugate of each individual entry. This operation is often used in conjunction with the transpose to form the conjugate transpose (also called the Hermitian transpose)
Matrices with Complex values, and computing conjugates are very common in signal processing and quantum mechanics.
Just like vectors, matrices also has a norm quantity defined. But unlike vectors, there are several types of norms for matrices. The method
norm in Sage returns the Frobenius norm which is defined as the square root of the sum of the squares of all the entries in the matrix.
