#Basic linear algebra project
rare frigateBOT
paper schooner
You assessment sounds right to me, though I don't remember linear algebra as well as other subjects.
but it finds the characteristic polynomialhttps://www.symbolab.com/solver/matrix-diagonalization-calculator/det%5Cbegin%7Bpmatrix%7D0-x%261%261.9%261.7%260%5C%5C%20%20%20%20%20%20.61%260-x%260%260%260%5C%5C%20%20%20%20%20%200%26.33%260-x%260%260%5C%5C%20%20%20%20%20%200%260%26.21%260-x%260%5C%5C%20%20%20%20%20%200%260%260%26.13%26.08-x%5Cend%7Bpmatrix%7D?or=input
which wolfram says has 5 distinct rootshttps://www.wolframalpha.com/input?i=0%3D+-x%5E5+%2B.08x%5E4+%2B0.61x%5E3+%2B+0.33367x%5E2%2B+0.0412665x+-0.005749128
ruby oxide
ah ez
well someone already mentioned it
but yeah you diagonalise it by finding its eigenvalues and eigenvectors and then u get a PDP^-1 decomposition
also known as the eigendecomposition
then your D matrix contains only diagonals. a Diagonal matrix to nth power is just its individual elements to the 10th power, making it easier
then you dot product the whole thing back to get the final matrix
E math help has the best calculators for most things check it out if u need it but perhaps u should also do it by hand at least once
tired ingot
we're supposed to do it by hand though... and finding eigenvalues involves finding determinants and the determinant of a 5x5 matrix is not something i'm willing to do
i've used websites and numpy and stuff and even went through papers on leslie matrices (and this doesn't even follow the proper form of one) and i literally can't find anything. this whole course has been incredibly easy though so i'm very confused if i'm just overlooking something really obvious
ruby oxide
we're supposed to do it by hand though... and finding eigenvalues involves findi...
change rows 1 and 2 and u should end up with an upper triangular matrix
then u can just multiply the diagonals for the deteriminants
but i think in that case, since u only have one non diagonal row, u can find a shortcut to solve eigenvalues and eigenvectors too
sadly i have now forgotten what that trick was
tired ingot
sorry am i going crazy or something? if i swap row 1 and 2, then the third row still would have a value on the second column which is below the diagonal so it's not an upper triangular matrix?
ruby oxide
yeah sorry my bad
i have forgotten all the tricks but i am sure there was a trick for eigen vectors for such situations
tired ingot
so far in this course the only things they've only covered very basic matrix operations... nothing even close to diagonalisation and eigenvectors and stuff. i've done linear algebra quite extensively before this so i don't mind using something more advanced but i'm confused what they expect me to do