Question
If $A$ is invertible and orthogonally diagonalizable, is $A^{-1}$ orthogonally diagonalizable as well?
Step 1
Step 1: Given that $A$ is invertible and orthogonally diagonalizable, we can write $A = SDS^{T}$ where $S$ is an orthogonal matrix and $D$ is a diagonal matrix. Show more…
Show all steps
Your feedback will help us improve your experience
Nick Johnson and 70 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
If $A$ is an invertible matrix that is orthogonally diagonalizable, show that $A^{-1}$ is orthogonally diagonalizable.
Suppose $A$ is invertible and orthogonally diagonalizable. Explain why $A^{-1}$ is also orthogonally diagonalizable.
Symmetric Matrices and Quadratic Forms
Diagonalization of Symmetric Matrices
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD