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I am doing some research and I want to use software like Scilab or MATLAB to plug in values for a, for example, $2\times 2$ matrix and see how the linear combination of vectors' direction and magnitude are changed when different numbers (or eigenvalues, etc). are manipulated. However I tried scilab and it is extremely hard and I don't know how to write matrices in scilab. In fact, what is the best software to do this in?

I can quickly clarify any unclearances.

I FORGOT TO ADD I HAVE A MACBOOK.

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  • $\begingroup$ In general, Maple (and probably Mathematica) are much easier to use than Matlab. The big exception is matrices. It is easier to define and manipulate matrices in Matlab, but it may be worth learning how to do it in Maple or Mathematica since just about everything else (such as plotting, derivatives, etc.) is so much harder in Matlab. $\endgroup$ – Stefan Smith Nov 11 '13 at 21:17
  • $\begingroup$ @StefanSmith: Why should I spend $140 when I can get what I need for free? $\endgroup$ – Don Larynx Nov 11 '13 at 21:22
  • $\begingroup$ Have you tried SAGE? $\endgroup$ – Bruno Joyal Nov 11 '13 at 21:46
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    $\begingroup$ @DonLarynx : my two cents: IMHO, Maple syntax is more natural and easier to learn than Mathematica syntax. In Maple, you just type what you want. Mathematica syntax has weird stuff like insisting on capital letters for command names and square braces, plus you have to type shift-enter to execute a command, not just enter (unlike every other programming language I've heard of). Many people prefer Mathematica and will give counterarguments. Either Maple or Mathematica will probably do everything you need. There are probably tons of beginner's guides to both freely available... $\endgroup$ – Stefan Smith Nov 11 '13 at 21:58
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    $\begingroup$ @DonLarynx : regarding Octave, I have heard that Octave can't really do symbolic computations at all. If this is important to you, you should check whether this is really the case before you try Octave. Matlab can do symbolic computations but not gracefully. With Maple or Mathematica, or course, symbolic computations are as easy or easier than numerical ones. $\endgroup$ – Stefan Smith Nov 11 '13 at 22:22
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IMHO you really could learn a lot from Mathematica, language is pretty simple and very connected to algebraic manipulations, also with very few knowledge of the language (even plain and simple English) you can do most of the computational stuff from calculus, linear algebra, complex analysis and discrete mathematics.

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  • $\begingroup$ Why should I pay $140 when I can get Octave, R, etc. for free? $\endgroup$ – Don Larynx Nov 11 '13 at 21:30
  • $\begingroup$ Where is a guide $\endgroup$ – Don Larynx Nov 11 '13 at 21:54
  • $\begingroup$ I use a licence from my university, I know that most colleges in the states have an agreement with wolfram, so usually for students enrolled at an university institution Mathematica is free, for a guide, I would recommend "programming with mathematica an introduction" from paul wellin. Also, you can find waldo with mathematica see: Link $\endgroup$ – David Cardozo Nov 12 '13 at 0:01
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I would recommend R. It is free, and very nice to do a lot of things with. Especially R Studio is recommended to use, the interface is one of the better ones I think.

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I would recommend Octave, its syntax is very similar to MATLAB and it is free.

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