### Questions (4)

 5 Prove that if A invertible and $\left\lVert A-B\right\rVert <\left\lVert A^{-1}\right\rVert ^{-1}$ then the following inequality holds 4 How to do a unitary diagonalization of a normal matrix? 2 Doolittle transformation is non-unique for singular matrices 1 A, B normal. Prove that A is similar to B if and only if the characteristic polynomials for A, B are the same.

### Reputation (250)

 +20 Are Doolittle's factorizations unique? +20 Prove that if A invertible and $\left\lVert A-B\right\rVert <\left\lVert A^{-1}\right\rVert ^{-1}$ then the following inequality holds +30 How to do a unitary diagonalization of a normal matrix? +10 Doolittle transformation is non-unique for singular matrices

 2 Are Doolittle's factorizations unique?

### Tags (8)

 2 matrices × 5 0 inequality 2 linear-algebra 0 matrix-calculus 2 numerical-methods 0 matrix-decomposition 0 diagonalization 0 norm

### Bookmarks (8)

 71 Difference between Fourier transform and Wavelets 39 When are minimal and characteristic polynomials the same? 28 Are idempotent matrices always diagonalizable? 28 What does "s.t." mean? 8 A quick way to estimate eigenvector/eigenvalue of a matrix