Eigenvalues and Diagonalization
The characteristic equation, trace as the sum and determinant as the product of eigenvalues, the 2 x 2 shortcut, eigenvectors, eigenvalues of powers, inverses, shifts, polynomials and transposes, eigenvalues by matrix type, row sums and the all-ones matrix, algebraic and geometric multiplicity, when a matrix is diagonalizable, similar matrices, the Cayley-Hamilton theorem for inverses and powers, and A^k through diagonalization, with every value checked in sympy.