[1.0] More linear algebra - the need for matrices and more functions in the vector

I was playing around with turtles and vectors found some essential algebra functions missing.

First:
[indent=1]To get the numbers of new calculated vectors, you need more than one command.[/indent]

vec = vector.new(1,2,3)

x, y, z = vec.x, vec.y, vec.z
-- or
x,y,z = split(vec.tostring, ",", 3)  -- from lua-users.org -wiki
-- instead of something like:
x,y,z = vec.getXYZ()

[indent=1]If I'm right, only this lines need to be added in the vector API:[/indent]

getXYZ = function( self )
return self.x, self.y, self.z
end

Second:
[indent=1]How about 3x3 matrices for vector transformation, multiplication and solving?[/indent]