Index Of The Matrix 1999 - Hot!

For an n×n integer matrix A, the index (also called the Smith–Minkowski–Smith index or simply index) of A often refers to the index of the subgroup generated by its column (or row) vectors inside Z^n: index(A) = [Z^n : im(A)]. Equivalently, if A has full integer rank n, index(A) = |det(A)|. If rank r < n, the index is infinite; instead one studies the absolute value of the product of the nonzero invariant factors (the determinant of any r×r maximal-rank minor), or the finite index of im(A) inside its saturation.

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As cultural symbol: Late 1999 was a hinge of expectation and anxiety — Y2K fears, end-of-century retrospectives, emergent internet cultures. “Matrix” evokes both the literal grids of information systems and the metaphoric web of mediated experience; “index” implies the act of pointing, choosing, ranking. Put together, the phrase can stand for the cataloging of a culture about to leap into the digital present: what gets indexed shapes what will be found, remembered, and valued in the decades to come. For an n×n integer matrix A, the index