Symmetric matrix - What is the symmetric matrix of the quadratic form
2x^2 - 8xy + 4y^2?
Similar Symmetric Diagonal Matrix - Suppose that A is a 2x2 matrix with real entries which is symmetric (A^t=A). Prove that A is similar over R to a diagonal matrix.
Matrix Theory - Show that each matrix type is normal.
1. Hermitian
2. skew-Hermitian
3. unitary
4. symmetric
5. skew-symmetric
6. orthogonal
Skew-symmetric matrix proof - please show work.
Give is a pxp skew-symmetric matrix S. Prove that S has purely imaginary eigenvalues. Prove that I + S is non-singular.