Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Kunze Linear Algebra · Problem 8.5.1
Inner Product Spaces
Mathematics — Methods · diagonalizing-real-symmetric-matrices
Problem For each of the following real symmetric matrices A A A P P P P t A P P^tAP P t A P [ 1 1 1 1 ] , [ 1 2 2 1 ] , [ cos θ sin θ sin θ − cos θ ] \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}, \quad \begin{bmatrix} 1 & 2 \\ 2 & 1 \end{bmatrix}, \quad \begin{bmatrix} \cos\theta & \sin\theta \\ \sin\theta & -\cos\theta \end{bmatrix} [ 1 1 1 1 ] , [ 1 2 2 1 ] , [ cos θ sin θ sin θ − cos θ ] Browse the problem library