Calculation of Matrices of Field Elements . Part
نویسندگان
چکیده
The articles [8], [3], [10], [11], [4], [1], [5], [2], [13], [6], [7], [12], and [9] provide the notation and terminology for this paper. In this paper i denotes a natural number. Let K be a field and let M1, M2 be matrices over K. The functor M1 −M2 yielding a matrix over K is defined by: (Def. 1) M1 − M2 = M1 + −M2. One can prove the following propositions: (1) For every field K and for every matrix M over K such that lenM > 0 holds −−M = M. (2) For every field K and for every matrix M over K such that lenM > 0
منابع مشابه
Calculation of Matrices of Field Elements . Part I
(4) Let K be a field and M1, M2, M3 be matrices over K. Suppose lenM1 = lenM2 and lenM2 = lenM3 and widthM1 = widthM2 and widthM2 = widthM3 and lenM1 > 0 and M1 + M3 = M2 +M3. Then M1 = M2. (5) For every field K and for all matrices M1, M2 over K such that lenM2 > 0 holds M1 − −M2 = M1 +M2. (6) For every field K and for all matrices M1, M2 over K such that lenM1 = lenM2 and widthM1 = widthM2 an...
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تاریخ انتشار 2007