Section 5.3 - Shelton State
... Gauss-Jordan Elimination We perform row-equivalent operations on a matrix to obtain a row-equivalent matrix in row-echelon form. We continue to apply these operations until we have a matrix in reduced row-echelon form. ...
... Gauss-Jordan Elimination We perform row-equivalent operations on a matrix to obtain a row-equivalent matrix in row-echelon form. We continue to apply these operations until we have a matrix in reduced row-echelon form. ...
7 Eigenvalues and Eigenvectors
... (1) Eigenvalues of a square matrix A are solutions of the equation χA (λ) = det (A − λI) = 0. (2)The null space of A − λI is equal to the eigenspace EA (λ) := {v : Av = λv} = N (A − λI). Proof: (1) If v is an eigenvector of A then v 6= 0 and Av = λv for some scalar λ. Hence (A − λI)v = 0. Thus the n ...
... (1) Eigenvalues of a square matrix A are solutions of the equation χA (λ) = det (A − λI) = 0. (2)The null space of A − λI is equal to the eigenspace EA (λ) := {v : Av = λv} = N (A − λI). Proof: (1) If v is an eigenvector of A then v 6= 0 and Av = λv for some scalar λ. Hence (A − λI)v = 0. Thus the n ...
