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A simple closed form for triangular matrix powers
| Content Provider | Semantic Scholar |
|---|---|
| Author | Shur, Walter |
| Copyright Year | 2011 |
| Abstract | 1. The algorithm. Huang [1] gives an algorithm for computing the powers of a triangular matrix where the diagonal elements are unique. However, in contrast to Huang’s algorithm, the method presented here has the unique advantage of producing the result in closed form, which shows explicitly how the behavior of any element of the matrix varies with varying powers of the matrix. Also, the closed form may be helpful in discovering or proving some other bound or relationship. Definition 1.1. Let M = [mi,j ] be a k× k upper triangular matrix with unique diagonal elements. We define the power factors of M , pi,j,s, recursively on the index j, as follows: |
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| Language | English |
| Access Restriction | Open |
| Subject Keyword | Algorithm Computation (action) Power (Psychology) Recursion The Matrix Triangular matrix |
| Content Type | Text |
| Resource Type | Article |
