```Hi -core,

I've commented matrix.rb, and in the process made the following

Matrix:
- initialize should be protected/private
- class methods could be wrapped in class << Matrix (matter of taste)
- the error mapping device is clumsy; why not just use normal exceptions?
- #slice would be a good alias for #minor
- it is possible to create uneven matrices (e.g. Matrix[ [1,2], [1] ].
This should be either disallowed, or at least a method should exist to
verify it.  The above matrix returns true for #square?, which is
disappointing.
- in general, some more exception handling should be added.  For instance,
Matrix[ [1,2], [1,2], [1,2] ].rank raises a low-level exception, not a
Matrix exception
- #compare_by_row_vectors should be private/protected
- #inverse_from should be private/protected?
- determinant of a non-square matrix should be an exception instead of 0?
- 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

Vector:
- initialize, init_elements should be private/protected
- eqn? should be eql?
- compare_by should be private/protected
- collect2 and map2 are different!
- #r should be something more normal, like #modulus (with #r an alias)
- BUG! Vector#coerce uses class Scalar, which doesn't exist in scope

Matrix::Scalar:
- what is the point of this class? (just curious)
- BUG! Scalar#** uses Matrix#powered_by

Gavin

```