The class of row monomial matrices (one unit and rest zeros in every row) with some non-standard operations of summation and usual multiplication is our main object. These matrices generate a space with respect to the mentioned operations. A word w of letters on edges of underlying graph of deterministic finite automaton (DFA) is called synchronizing if w sends all states of the automaton to a unique state J. \v{C}erny discovered in 1964 a sequence of n-state complete DFA possessing a minimal synchronizing word of length (n-1)(n-1). The hypothesis, well known today as the \v{C}erny conjecture, claims that (n-1)(n-1) is also precise upper bound on the length of such a word for a complete DFA. The hypothesis was formulated in 1966 by Starke. The problem has motivated great and constantly growing number of investigations and generalizations. We present the proof of the \v{C}erny-Starke conjecture: the deterministic complete n-state synchronizing automaton has synchronizing word of length at most (n-1)(n-1). The proof used connection between dimension of the space and the length of words on paths of edges in underlying graph of automaton.

翻译：单体矩阵( 单体矩阵和每行零位和零位) 类别, 具有某些非标准的总和和和通常乘法操作, 是我们的主要对象。 这些矩阵生成了与上述操作有关的空间。 在确定性自定义自动图( DFA) 底图边缘的字母值是同步的。 如果将自动图的所有状态发送到一个独特的状态J.\v{C}}erny 发现1964年的N- state 完整的 DFA序列, 具有最小同步的长度( n-1( n-1) ) 。 假设, 现今又被称为\v{C} erny 推测, 声称( n-1) 也精确地将这种单词的长度与完整的 DFA 。 假设是1966年 Starke 制定的。 问题促使大量且不断增长的调查和概括。 我们展示了N- v{C} Stake 直观信号: 确定性全正态同步的 n- sn- 同步化同步化的自动直径连接到最长的磁度路径的磁度 。