CM0368 Scientific Computing
... • An elementary matrix, M, is one that has 1’s along the main diagonal and 0’s everywhere else, except for one non-zero value (-m, say) in row i and column j. • Multiplying A by M has the effect of subtracting m times row j of matrix A from row i. • Ignoring pivoting, the GE algorithm applies a seri ...
... • An elementary matrix, M, is one that has 1’s along the main diagonal and 0’s everywhere else, except for one non-zero value (-m, say) in row i and column j. • Multiplying A by M has the effect of subtracting m times row j of matrix A from row i. • Ignoring pivoting, the GE algorithm applies a seri ...
26. Examples of quotient rings In this lecture we will consider some
... This means that the map ι : Z/nZ → Zn given by (***) is (a) well-defined (b) bijective (c) preserves group operation (addition), that is, ι((x + nZ) + (y + nZ)) = ι((x + y) + nZ) for all x, y ∈ Z We claim that ι is actually a ring isomorphism. In view of (a), (b) and (c) it remains to check that ι a ...
... This means that the map ι : Z/nZ → Zn given by (***) is (a) well-defined (b) bijective (c) preserves group operation (addition), that is, ι((x + nZ) + (y + nZ)) = ι((x + y) + nZ) for all x, y ∈ Z We claim that ι is actually a ring isomorphism. In view of (a), (b) and (c) it remains to check that ι a ...
