Descomposición de una matriz cuadrada compleja como una suma finita de matrices idempotentes
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Date
2024
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Universidad Nacional de Trujillo Añadir
Abstract
El presente trabajo de investigaci´on titulado “Descomposici´on de una matriz cuadrada compleja como una suma finita de matrices idempotentes”, es la continuación de un trabajo desarrollado por R.E. Hartwig y M.S. Putcha e independientemente por P.Y. Wu, quienes establecieron que una matriz cuadrada compleja es una suma finita de matrices idempotentes si y sólo si tr T es un entero y tr T ≥ rank T. Lo que se pretende hacer aquí, es determinar el número mínimo de matrices idempotentes para tales matrices en términos de sus trazas, y nos ocupamos de resolver el problema completamente para matrices de orden 2, 3, 4 y 5 y también damos algunas condiciones suficientes y necesarias para que una matriz cuadrada compleja sea la suma de tres o mas idempotentes. Formulando lo previamente mencionado, consideramos una matriz Tn×n, donde T = E1 + E2 + ... + Em, con E2i = Ei, para i = 1, ...,m y tr T un entero mayor o igual que rank T, y a partir de aquí determinar las condiciones necesarias y suficientes para que el número de idempotentes requeridas sea el mínimo
Abstract The present research work entitled “Decomposition of a complex square matrix as a finite sum of idempotent matrices”, is the continuation of a work developed by R.E. Hartwig and M.S. Putcha and independently by P.Y. Wu, who established that a complex square matrix is a finite sum of idempotent matrices if and only if tr T is an integer and tr T ≥ rank T. What we are trying to do here is to determine the minimum number of idempotent matrices for such matrices in terms of their traces, and we deal with to solve the problem completely for matrices of order 2, 3, 4 and 5 and we also give some sufficient and necessary conditions for a complex square matrix to be the sum of three or more idempotents. Formulating the previously mentioned, we consider a matrix Tn×n, where T = E1+E2+...+Em, with E2i = Ei, for i = 1, ...,m and tr T an integer greater than or equal to rank T, and from here ´ı determine the necessary and sufficient conditions for the n´u The number of idempotents required is the minimum
Abstract The present research work entitled “Decomposition of a complex square matrix as a finite sum of idempotent matrices”, is the continuation of a work developed by R.E. Hartwig and M.S. Putcha and independently by P.Y. Wu, who established that a complex square matrix is a finite sum of idempotent matrices if and only if tr T is an integer and tr T ≥ rank T. What we are trying to do here is to determine the minimum number of idempotent matrices for such matrices in terms of their traces, and we deal with to solve the problem completely for matrices of order 2, 3, 4 and 5 and we also give some sufficient and necessary conditions for a complex square matrix to be the sum of three or more idempotents. Formulating the previously mentioned, we consider a matrix Tn×n, where T = E1+E2+...+Em, with E2i = Ei, for i = 1, ...,m and tr T an integer greater than or equal to rank T, and from here ´ı determine the necessary and sufficient conditions for the n´u The number of idempotents required is the minimum
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Matrices idempotentes, traza de una matriz, rango de una matriz