%. x for a vector x is the same as ($x)$%.,.x, and the key expression is
%.,.x, the "matrix inverse" of a 1-column matrix. b=.y%.x on a tall matrix
x is solving a least-squares problem, the coefficients b that minimizes the
sum of squares of y - x +/ .* b .
In addition, for a non-zero vector x, (%.x) +/ .* x is 1, a special case of
that (%.x)+/ .* x is an identity matrix, whence one can deduce that for
vector x, %.x is x%+/x^2.
] x=: 7 ?.@$ 100
94 56 8 6 85 48 66
%. x
0.00362137 0.00215741 0.000308202 0.000231152 0.00327465 0.00184921
0.00254267
(%.x) +/ .* x
1
x % +/x^2
0.00362137 0.00215741 0.000308202 0.000231152 0.00327465 0.00184921
0.00254267
M=: 7 3 ?.@$ 100
(%.M) +/ .* M
1 5.55112e_17 _2.77556e_17
_1.21431e_16 1 1.11022e_16
_4.85723e_17 1.94289e_16 1
On Wed, Apr 23, 2014 at 9:13 AM, alexgian <[email protected]> wrote:
> Just wondering:
> %. 2 3 4
> 0.0689655 0.103448 0.137931
>
> Which is fair enough enough at one level, I suppose, since the dot product
> of the two arrays IS 1, but what system/equation is being solved here?
> Obviously, there are infinite solutions. Why that one?
> IOW, which "matrix" is being inverted here?
>
> Thanks
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