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Explicit solutions of the Yang–Baxter-like matrix equation for an idempotent matrix

open access: yesApplied Mathematics Letters, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qianglian Huang, Jiu Ding
exaly   +4 more sources

k-Idempotency of linear combinations of an idempotent matrix and a tripotent matrix that commute

open access: yesIndian Journal of Pure and Applied Mathematics, 2011
The authors establish a complete solution to the problem of characterizing all situations in which a linear combination \(C=c_1A+c_2B\) of an idempotent matrix \(A\) and a tripotent matrix \(B\) is \(k\)-idempotent. As a special case of this, a set of necessary and sufficient conditions for a linear combination \(C=c_1A+c_2B\) to be \(k\)-idempotent ...
Krishnamoorthy, S., Rajagopalan, T.
exaly   +3 more sources
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When is a matrix a sum of idempotents?

Linear and Multilinear Algebra, 1990
It is shown that a matrix A, ovei a field of characteristic zero, is a sum of idempotents. exactly when the trace of A is an integer at least as large as rank(A).
Robert E. Hartwig, Mohan S. Putcha
openaire   +1 more source

Solutions of the Yang-Baxter matrix equation for an idempotent

open access: yesNumerical Algebra, Control and Optimization, 2013
Let $A$ be a square matrix which is an idempotent. We find all solutions of the matrix equation of $AXA=XAX$ by using the diagonalization technique for $A$.
Jiu Ding, Noah H Rhee
exaly   +2 more sources

On the equality between rank and trace of an idempotent matrix

Applied Mathematics and Computation, 2010
The paper deals with the question whether it is possible to derive the equality between the rank and trace of an idempotent matrix by using only the idempotency property, without referring to any further features of the matrix. It is shown that such a proof can be obtained by exploiting a general characteristic of the rank of any matrix.
Oskar Maria Baksalary   +2 more
openaire   +2 more sources

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