| Matrix Algebra Motivated by Essentially Stochastic Matrices |
| Received:September 08, 1984 |
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| Abstract: |
| A matrix of order n whose row sums are all equal to 1 is called an essentially stochastic matrix (see Johnsen [4]). We extend this notion as the following. Let F be a field of characteristic 0 or a prime greater than n. Mn(F) denotes the set of all n×n matrices over F. Let t be an elernent of F. A matrix A=(aij) in Mn(F) is called essentially t-stochastic' provided its row sums are each equal to t. We denote by Rn(t) the set of all essentially t-stochastic matrices over F. We shall mainly study Rn(0) and Rn(F)=(?)Rn(t). Our main references are Johnson [2,4] and Kim [5]. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1987.04.005 |
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