What is the name (if any does exist) of an upper-triangular matrix whose elements on each diagonal are equal? Also, are there any properties associated with this matrix or not?
Thanks in advance for your help.
2026-03-25 00:25:06.1774398306
Name of a specific upper-triangular matrix
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You're asking about upper triangular Toeplitz matrices. Here is a post about inverting them, and here is an article about factorizing them.
It is notable that every such matrix can be written as a polynomial of the matrix $$ M = \pmatrix{0&1&0\\0&0&1&0\\&&\ddots&\ddots&\\ &&&&1\\ &&&&0} $$ and that any two such matrices commute.