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Non-graphing calculator supporting complex matrices?
04-27-2014, 05:33 PM
Post: #16
RE: Non-graphing calculator supporting complex matrices?
(04-27-2014 05:36 AM)Manolo Sobrino Wrote:  
(04-27-2014 03:59 AM)supernumero Wrote:  Good question. I did not mean to say I had used the 15C for this purpose; I was merely referring to the fact that the 15C supported complex matrices, and it is necessary to deal with complex matrices to find complex eigenvectors (even of real matrices). (I'm assuming the eigenvalues have already been found by some method---think of a 3x3 matrix whose real eigenvalue can be SOLVEd for, leading to a quadratic for the remaining pair of possibly complex eigenvalues. There would still remain the problem of finding the complex eigenvectors.)
... and you never worked out the algebra of how doing this with 2 systems of linear equations and just real numbers, just in case you want to use a cheap calculator, that in any case can't help you with the homogeneous system. I don't think that you or your students really need a calculator.

Ouch! Summary judgment alert!

The proximate reason I started this thread was solving an exercise straight from Boyce-DiPrima's book to present in a lecture:

Find the general solution to the system:
\( x'_1 = -3x_1 + 2x'_3 \)
\( x'_2 = x'_1-x'_2 \)
\( x'_3 = -2x'_1-x'_2 \)

or \(\mathbf{x}' = A\mathbf{x} \) in matrix-vector notation.

The characteristic values of \(A\) are \(\lambda = -2, -1\pm\sqrt2i.\) The eigenvectors are obtained by solving the singular homogeneous linear 3x3 systems \((A-\lambda I)\xi = \mathbf{0},\) which is a simple enough task but (even in the real case) is beyond the functionality cheap calculators (entirely for non-intrinsic reasons such as hardware limitations). I did the calculations by hand: They are, of course, completely routine, but it's quite easy to make mistakes.

SN
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