Bug in EIGENVV in combination with built-in matrices M0..M9 in 10077

[Arno K]

Today I came across the task of getting a matrix simplified with different ways to perform, one was M= [[2,0,0,0],[2,2,0,0],[1,-1,2,-1],[0,1,0,2]], a Schur decomposition was to be done and this is provided by the Prime.
As I want to check out the Prime's capabilities I tried to get the eigenvalues, easily computed by hand, all are 2, the Prime gives a warning ( "Low accuracy" ) and using EIGENVAL(M3), provides 4 values which can be rounded to 2.
Then I tried EIGENVV(M3) and the physical prime simply restarted, the PC-emulator halted (both latest firmware) and the Android-app (8151) crashed, too. Recalling M3 and EIGENVV(Ans) delivers: "Not invertible error: Bad Argument Value", contrary to Wolfram, saying [0,0,1,0] is an eigenvector and that is correct.
Arno

[parisse]

Crashed again because the Prime does not have exceptions, it returns a "not invertible error" on Xcas (this is expected because the matrix is not diagonalizable, therefore numeric diagonalization will fail while exact diagonalization works).

[compsystems]

MATHEMATICA
https://www.wolframalpha.com/input/?i=EI...0,2%5D%5D)
[2,2,2]

TI68K
EIGVL([[2,0,0,0],[2,2,0,0],[1,-1,2,-1],[0,1,0,2]]) [enter]
[2,2,2]


hpprime
EIGENVAL([[2,0,0,0],[2,2,0,0],[1,-1,2,-1],[0,1,0,2]]) [enter]
"Low accuracy" then [2.00058131764,1.99961844696, 2.00018411644, 1.99961611895]
https://www.wolframalpha.com/input/?i=EI...0,2%5D%5D)

Prime does not have exceptions???
So, why not incorporated?

[parisse]

You can get exact eigenvalues inside the CAS, even more jordan will return the Jordan normal form (not available on the ti).

Code:

p,j:=jordan([[2,0,0,0],[2,2,0,0],[1,-1,2,-1],[0,1,0,2]]); p*j*inv(p);

EIGENVV etc. are numeric diagonalization instructions, they are expected to fail with non diagonalizable matrices (otherwise it means that the algorithm used is not purely numeric, if it works on the ti, it might mean that the ti is using the characteristic polynomial to find eigenvalues, very bad for numeric stability).

[Arno K]

Well, I did not (really) bother about the prime not being able to produce the eigenvectors, what I wanted to say is: it CRASHED using EIGENVV(M3) where M3 is one of the built-in matrices filled with the data provided above here the warning: Matrix is not diagonalizable, try.... would be a workaround.
Arno

[parisse]

Of course it should not crash, it's now fixed in the source code.