Bool阵的逆阵

We give a characterization of a regular Boolean matrix and prove that AB = I Implies that BA = I, where A and B are Boolean matrices whose elements belong to a Boolean algebra of a set with more than two elements.     

On r-potent linear mappings

Let L(E) be the set of all linear mappings of a vector space E. Let Z₊ be the set of all positive integers. A nonzero element ? in L(E) is called an r-potent if $\text{?}{}^{\mathrm{r}}\text{=?}\text{and}\text{?}{}^{\mathrm{i}}\text{≠?}\text{for}\text{1<i<r (i,r∈Z}{}_{\mathrm{+}}\text{)}$. We prove that $\text{S(E)= {?∈L(E): ?}\text{is singular}\text{}}$ is a semigroup generated by the set of all r-potents in S(E), where r is a fixed positive integer with 2?r?n=dim(E).     

On the number of idempotent linear transformations

Let M and N be two subspaces of a finite dimensional vector space V over a finite field F. We can count the number of all idempotent linear transformations T of V such that R(T) ?M and N?N(T), where R(T) and N(T) denote the range space and the null space of T, respectively.     

On the structure of linear semigroups

Green's Lemma [1, Lemma 2.2] is one of the most important theorems in the theory of semigroups. The main purpose of this note is to establish a generalized Green's Lemma and a generalized Clifford and Miller's Theorem [1, p. 59] in linear semigroups. A generalized Green's Lemma describes the behavior of certain mappings between two distinct D-classes.     

由本性随机阵导致的陈代数

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. M_n(F) denotes the set of all n×n matrices over F. Let t be an elernent of F. A matrix A=(a_ij) in M_n(F) is called essentially t-stochastic' provided its row sums are each equal to t. We denote by R_n(t) the set of all essentially t-stochastic matrices over F. We shall mainly study R_n(0) and R_n(F)=(?)R_n(t). Our main references are Johnson [2,4] and Kim [5].     

实幂等矩阵的伴随矩（英）

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