The '''spectral theorem''' states that a [[symmetric matrix]] is orthogonally diagonalizable, and vice-versa. This is the one the most fundamental theorems in [[linear algebra]], and is frequently used to solve problems. | The '''spectral theorem''' states that a [[symmetric matrix]] is orthogonally diagonalizable, and vice-versa. This is the one the most fundamental theorems in [[linear algebra]], and is frequently used to solve problems. |