Revision as of 03:48, 28 July 2025 edit Goodphy (talk \| contribs) Extended confirmed users 1,952 edits Removed an unnecessary word. Tags: Reverted Visual edit ← Previous edit		Revision as of 04:00, 28 July 2025 edit undo Goodphy (talk \| contribs) Extended confirmed users 1,952 edits →The Algorithm: Added the reason why c_n = 1. Tag: Visual edit Next edit →
Line 9: The objective is to calculate the coefficients {{math\|''c<sub>k</sub>''}} of the characteristic polynomial of the {{math\|''n''×''n''}} matrix {{mvar\|A}}, ::<math>p_A(\lambda)\equiv \det(\lambda I_n-A)=\sum_{k=0}^{n} c_k \lambda^k~,</math> where, evidently, {{math\|''c<sub>n</sub>''}} = 1 ~~and~~(characteristic polynomials are [[Monic polynomial\|monic polynomials]]) and {{math\|''c''}}<sub>0</sub> = (−1)<sup>''n''</sup> det {{mvar\|A}}. The coefficients {{math\|''c<sub>n-i</sub>''}} are determined by induction on {{mvar\|i}}, using an auxiliary sequence of matrices

Faddeev–LeVerrier algorithm: Difference between revisions