Recall that if v is a non-zero vector such that Mv = av, for a scalar a, then v is called an eigenvector corresponding to the eigenvalue a.
i1 : M = matrix{{1, 2}, {5, 7}} o1 = | 1 2 | | 5 7 | 2 2 o1 : Matrix ZZ <--- ZZ |
i2 : eigenvectors M o2 = ({-.358899}, | -.827138 -.262266 |) {8.3589 } | .561999 -.964996 | o2 : Sequence |
i3 : M = matrix {{1, 2}, {2, 1}} o3 = | 1 2 | | 2 1 | 2 2 o3 : Matrix ZZ <--- ZZ |
i4 : (e,v) = eigenvectors(M, Hermitian=>true) o4 = ({-1}, | -.707107 .707107 |) {3 } | .707107 .707107 | o4 : Sequence |
i5 : class \ e o5 = {RR} {RR} o5 : VerticalList |
i6 : v o6 = | -.707107 .707107 | | .707107 .707107 | 2 2 o6 : Matrix RR <--- RR 53 53 |
The object eigenvectors is a method function with options.