Given that $x$ and $y$ are column vectors and $A$ is a matrix, I figured out the result $y^{T}y-2y^{T}Ax +x^{T}A^{T}A\,x$
I want to use Mathematica to make such calculations. how do I enter them into a notebook?
Below is my attempt
![1]](https://i.sstatic.net/iAExz.jpg)
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1$\begingroup$ It would be beneficial if you could show what you have already tried with a short description why it does not fulfil your requirements. This would allow others to give you a better answer. $\endgroup$– e.doroskevicCommented Dec 7, 2015 at 12:48
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$\begingroup$ This may be a duplicate of: mathematica.stackexchange.com/q/3242/131 and/or mathematica.stackexchange.com/q/52213/131 (both deal with symbolic vector notation). $\endgroup$– Yves KlettCommented Dec 7, 2015 at 13:01
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$\begingroup$ Also relevant: mathematica.stackexchange.com/a/40368/242 (esp. the first three paragraphs) $\endgroup$– Niki EstnerCommented Dec 7, 2015 at 15:00
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1 Answer
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Without the addition of third-party symbolic algebra packages, Mathematica does symbolic algebra best with definite dimensions. You can do things like
With[{m = 3, n = 4},
Module[{A, xx, yy},
A = Array[a, {m, n}];
xx = Array[x, n];
yy = Array[y, m];
(yy - A.xx).(yy - A.xx)]]
(-a[1, 1] x[1] - a[1, 2] x[2] - a[1, 3] x[3] - a[1, 4] x[4] + y[1])^2 + (-a[2, 1] x[1] - a[2, 2] x[2] - a[2, 3] x[3] - a[2, 4] x[4] + y[2])^2 + (-a[3, 1] x[1] - a[3, 2] x[2] - a[3, 3] x[3] - a[3, 4] x[4] + y[3])^2
Note that Mathematica does not distinguish between row and column vectors and will not transpose vectors.
answered Dec 7, 2015 at 14:15