matrix algebra applications?
918671
Computer programming\nImage editing\nSearch Engines (Google, for example, has a search matrix of the order 2.7 billion)
1802
I haven't tried it, but check out MatPy (linked below).  Another possibility is Numerical Python (also linked below).
85187
I don't really know what you need help on....\n\nCheck out some of the sites below in the source section, or you could just post what in particular is troubling you...\n\n(I can sympathize if you're having trouble with Matrices though... those always have so many places to go wrong.. ugh.)\n\n(PPS: Wikipedia can be very useful for finding out more information, as you can tell from the number of links below.)
20441
Linear algebra deals with linear vector spaces. Operations on linear vector spaces are limited to additon of two vectors and multiplication of a vector by a constant. Matrix algebra is a subset of linear algebra.\n\nIf X, Y, and Z are vectors, aX + bY = Z has meaning\nbut aX^2 + bY^2 = Z does not.
1062782
you should use matlab.
603045
spell correct\n\nhttp://www.matrixewebs.com
945015
Modal analysis is one application of Eigenvalue analysis but Eigenvalue analysis can be used for other things.\n\nIn the context of modal analysis (using FEM), the eigenvalue=eigenfrequency=natural frequency (mode).\n\nThe eigenvector is the diplacement vector or mode shape of the mode.\n\nI haven't seen the term eigensystem, but it probably refers to the matrix and vector for the problem (i.e. everything as a whole).
415924
A matrix is an array of numbers that is usually studied in relation to solving systems of equations and more general problems in linear algebra. Familiarity with linear algebra is the gateway to higher mathematics; the matrix part of this is little more than advanced arithmetic.
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http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/\n\nhttp://www.math.armstrong.edu/MathTutorial/
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Diagonalisation is the answer here.  Not sure how this didn't turn up in a web search, as I found plenty of resources for it, but the idea is that you find a matrix that diagonalises your initial matrix, and this allows powers to be done trivially.\n\nAssuming you're aiming to get a matrix A to the power n:\n\nFind P such that:\nP^-1 A P = D, where D is diagonal.  Then:\nA = (P D P^-1) and:\nA^n = (P D P^-1)(P D P^-1)(P D P^-1)....\n\nThe P^-1 P terms cancel and you're left with:\nA^n = P D^n P^-1\n\n... and this is much easier to calculate as D^n is trivial :)\n\nA good reference is in the sources.  Hope that helps!
1079454
The previous answers are all WRONG. It is not easy to give a general formula, but here is the definition and the proceedure:\n\nFirst of all, remember that the power series expansion of sin x is\nsin x=x -(1/6) x^3 +(1/120)x^5-+...\n\nIf you plug in At for x, you get\nsin(At)=At-(t^3/6)A^3 +(t^5/120)A^5-+...\n\nThe powers here are obtained by matrix multiplication. For a *diagonal* matrix, you can simply take the sine of the diagonal entries (as the previous posters suggested), but that doesn't work for non-diagonal matrices. It should be pointed out that exp(At) or cos(At) would be defined by power series in a similar way.\n\nIn most applications, the matrix A is symmetric, so can be diagonalized (by finding eigenvalues, etc). In this case, there is\na diagonal matric D and another matrix P so that\nA=PDP^{-1}.\nThe matrix D has the eigenvalues of A along the diagonal and the matrix P has the corresponding eigenvectors down the columns.\nAnyway, for such matrices,\nsin(At)=P{sin(Dt)]P^{-1}.\nSince sin(Dt) is easy, this allows the computation of sin(At).\n\nFor non-diagonalizable matrices, the computation is harder.
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Anyone with matrix background
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This normally means that you are going to be using Gaussian (or Gauss-Jordan) reduction, where ther eare three "moves" that are allowed.\n\n1) You can switch any two rows in the matrix.\n2) You can multiply any row in the matrix by a non-zero scalar.\n3) You can add a multiple of one row to another.\n\nUsing these three "moves," the goal is to reduce the matrix into a usable form (the echelon form, for example).
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There is a primer here:\nhttp://www.phon.ucl.ac.uk/courses/spsci/matlab/primer40.pdf\n\nand an online course here:\nhttp://www.phon.ucl.ac.uk/courses/spsci/matlab/\n\nI may just be reviewing them myself!
1075376
wow..that site http://www.algebra.com/services/renderin... is really amazing. You can also check out mupad. It will do simplifications and give answers to integration and much more. There's a demo available at http://www.sciface.com/
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http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut35_polyfun.htm\n\nhttp://www.sosmath.com/algebra/algebra.html\n\nI found these to be helpful.
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you should try to learn reading any book about vector analysis.\nSomething about vectors:\nhttp://mathworld.wolfram.com/topics/VectorAlgebra.html