On Mon, 20 Jan 2003, Gavin Sinclair wrote:
>  - #slice would be a good alias for #minor

The problem with #minor is that it's not a minor, it's a slice.

A minor is a submatrix such that only one row and one column are missing.
The #minor operation allows only 4 possible minors, out of 2*N, and allows
lots of things that are not minors.

>  - Matrix#diagonalize() should return a [M:Matrix,D:Matrix] pair such that
>    M*D*M.inverse == self
>  - ** is too slow.  Using matrix diagonalisation is a more efficient algorithm
>    and works for all exponents, not just positive integers.  Here is a more
>    efficient **
>            def ** n
>                 m, d = diagonalize
>                 (0...d.row_size).each { |i| d[i,i] **= n }
>                 (m * d * m).inverse
>            end

This is not the code I gave you. I wrote m*d*m.inverse, not
(m*d*m).inverse; the parentheses make a big difference.

Also: I made a mistake. Some matrices are not diagonalizable, so there
should be a fallback to another algorithm. That one can be the existing
one, running in O(k*n**3), or it can be a new one, running in
O(log(k)*n**3), following the same pattern as the implementation of
Bignum#**.

(of course those O() marks are slightly wrong, as they depend on the speed
of a lot of other methods that may or may not run in their assumed times)

>  - #r should be something more normal, like #modulus (with #r an alias)

#abs is good, especially because (x-y).abs on vectors is a metric.
(see http://mathworld.wolfram.com/Metric.html)

However it wouldn't be good to think of a matrix determinant as an
absolute value, despite mathematicians using the same notation... one
reason is that a det can be negative, while abs's are expected not to.

________________________________________________________________
Mathieu Bouchard                       http://artengine.ca/matju