Check whether a square matrix commutes with its own transpose (A·Aᵀ = Aᵀ·A).
How It Works
How Normal Matrix Checker Works
The calculator multiplies the matrix by its transpose both ways round — A times Aᵀ, and Aᵀ times A — and checks whether the two results match exactly.
FAQ
Frequently Asked Questions
Why does this property matter in linear algebra?
Normal matrices are exactly the ones that can be fully diagonalized using an orthonormal set of eigenvectors — a well-behaved property that a lot of matrix theory depends on.
Are symmetric matrices always normal?
Yes — for a symmetric matrix, A equals Aᵀ, so A·Aᵀ and Aᵀ·A both reduce to A·A, meaning they're automatically equal.
