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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.

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  • $\begingroup$ They are a constant multiple of unipotent matrices, which are matrices $A$ such that $A-I$ is nilpotent, i.e. $(A-I)^{m} = O$ for some $m>0$. $\endgroup$ – Seewoo Lee May 26 at 0:00
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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.

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