chaotixmonjuish said:Ok, so I had a rationale why it was false but I'm not sure if I am close.
Obviously here the AT does not equal A, but the dimension of the row space equals column space equals 2. Is this the right reasoning?
A symmetric matrix is a square matrix that is equal to its transpose. In other words, it is a matrix that is symmetric along its main diagonal.
Some important properties of a symmetric matrix include: it has equal eigenvalues, it is diagonalizable, and its eigenvectors are mutually orthogonal.
To determine if a matrix is symmetric, you can check if it is equal to its transpose. If the elements are the same when reflected across the main diagonal, then it is symmetric.
Symmetric matrices have many applications in mathematics, including in linear algebra, optimization, and statistics. They are also important in physics and engineering, where they are used to represent real-world systems.
Some examples of symmetric matrices include identity matrices, diagonal matrices, and matrices with all equal elements. In real-world applications, symmetric matrices can be used to represent symmetric systems, such as in mechanics or quantum mechanics.