Let be an eigenvalue of the nonsingular matrix A with associated eigenvector . Show that is an eigenvalue of with associated eigenvector . Things I thought about: roots of are eigenvalues, inverse is calculated by rref[A|In]
Last edited by Jskid; Mar 29th 2011 at 12:19 PM. Reason: solved
Follow Math Help Forum on Facebook and Google+
Originally Posted by Jskid Let be an eigenvalue of the nonsingular matrix A with associated eigenvector . Show that is an eigenvalue of with associated eigenvector . Things I thought about: roots of are eigenvalues, inverse is calculated by rref[A|In] you know that there exists some such that so that or (where we used the fact that is invertible thus )
Originally Posted by Drexel28 or But you can't divide by a vector or matrices, in this case ? Are you allowed to multiply by its reciprocal?
Originally Posted by Jskid But you can't divide by a vector or matrices, in this case ? Are you allowed to multiply by its reciprocal? Huh? I'm sorry I must be misuderstanding you. Isn't a scalar?
Originally Posted by Drexel28 Huh? I'm sorry I must be misuderstanding you. Isn't a scalar? I thought it was a vector but it turned out I was confused
View Tag Cloud