✦ LIBER ✦
A criterion for unitary similarity of upper triangular matrices in general position
✍ Scribed by Douglas Farenick; Vyacheslav Futorny; Tatiana G. Gerasimova; Vladimir V. Sergeichuk; Nadya Shvai
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 269 KB
- Volume
- 435
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
✦ Synopsis
Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A = [a ij ] and B = [b ij ] be upper triangular n × n matrices that
• are not similar to direct sums of square matrices of smaller sizes, or
• are in general position and have the same main diagonal.
We prove that A and B are unitarily similar if and only if
j=1 and B k := [b ij ] k i,j=1 are the leading principal k × k submatrices of A and B, and • is the Frobenius norm.