1 votes 1 votes Characteristic roots of matrix $A$ and $A^T$ will be a) Different b) Same c) Cannot say about roots d) None of these Linear Algebra isro-ee matrix + – sh!va asked Mar 10, 2017 edited Mar 7, 2019 by Naveen Kumar 3 sh!va 751 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
3 votes 3 votes Option B is correct. det(AT−λI) = det ( (A−λI)T ) = det(A−λI) From this it is obvious that the eigenvalues or characteristic roots are the same for both A and AT. Transpose of A is AT. Transpose of (A−λI) is (A−λI)T Shubham Sharma 2 answered Mar 10, 2017 edited Mar 10, 2017 by Shubham Sharma 2 Shubham Sharma 2 comment Share Follow See 1 comment See all 1 1 comment reply Prince Singh 1 commented Oct 30, 2018 reply Follow Share I think answer should be (c) can't say about roots. because what about orthogonal matrices i.e. AT = A-1 tells eigenvalues of AT are same as eigenvalues of A-1 but eigenvalues of A-1 are reciprocal of eigenvalues of A, then eigenvalues of AT will be reciprocal of A ? Or, are eigenvalues of A-1 and A same if A is orthogonal ? if yes then eigenvalues will always be 1. 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Transpose of matrix does not change the root of the matrix. Manashi Sarkar answered Apr 30, 2017 Manashi Sarkar comment Share Follow See all 0 reply Please log in or register to add a comment.