Numerical Linear Algebra
where the algebra stops being the arithmetic
Ladder

Normal forms — the ladder

One essay so far against this idea. A ladder is the distinct arguments that stand against one idea, and this one has room to grow.
  1. s10 bitss20 bitss30 bitss40 bitss514 bitsinvariant factors, in bitstwo routes, and a conserved quantitydet A-2.3·10⁴Π invariants2.3·10⁴SNF widest15HNF widest24det of the transform-1an algorithm and a definitionagreeing as integers

    What a determinant does not determine

    Two integer matrices can have the same determinant, the same rank and the same size, and define genuinely different maps. What separates them is a list of integers each dividing the next — computed here twice, once by unimodular elimination and once from the gcds of every minor, which share no algorithm at all.

    rung 1 · exact

All ladders