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Matrix mathematics

Chaotic42

Chaotic42

Lifer
I don't really know how to phrase this question, but I'm curious so I'll take a shot.

Is there any significance to the two-dimensionality of the matricies that we use in mathematics?

Is there any system of equations that would require the use of a cubic (or n-dimensional) matrix? For example, instead of a standard nxn matrix, you would have an nxnxn matrix.

Does such a thing exist?
 
I can't think of a specific instance save for this one in the EE field. The Karnaugh map when dealing with a lengthy bit-string is a 2d-map that can have several layers. You could call this an nxnxn matrix, you can simplify between layers (in the 3rd dimension)
 
The Fortran language allows you to specify arrays with up to 9 indicies (or dimensions). It is all about storing data. The first application that comes to mind is storing data for superheat steam tables. Different data sets at different temperatures and pressures would benefit from a multi-dimensional storing scheme.

R
 
Many physical systems are multi-dimensional in this manner. If you think about it this way, each dimension of a matrix represents a variable. So, as rgwalt said regarding steam tables, one dimension of the matrix can be pressure, one is temperature, and the other is composition. Thus, you have 3 dimensions in your matrix. You can go to much higher dimensions in this manner as well (infinitely many really), though it's pretty much impossible to visualize and only exists as a mathematical construct at that point.
 
Yes, EEs use matrix math, especially those involved in control systems design.


In control theory, when multiple inputs and outputs are involve in a system, the only sane way to model and control that system is to use the state-space approach which involves matrix math & linear algebra.
 
Originally posted by: Chaotic42
I don't really know how to phrase this question, but I'm curious so I'll take a shot.

Is there any significance to the two-dimensionality of the matricies that we use in mathematics?

Is there any system of equations that would require the use of a cubic (or n-dimensional) matrix? For example, instead of a standard nxn matrix, you would have an nxnxn matrix.

Does such a thing exist?
Click to expand...
A map between finite dimensional linear spaces is naturally represented by a n*m matrix. Now if you want to map a third space l into the space of linear maps you could take the natural basis and have an l*(n*m) matrix but it would be more sensible just to have an l*n*m matrix. Differentiating functions between linear spaces can have you picking up dimensions.
 
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