I just want to know how D is calculated. Thanks!
Posted: Fri Jul 01, 2022 5:29 am
I just want to know how D is calculated.
Thanks!
-100 0 0-10 0 5 4-5 00-1 The objective is to find an invertible matrix P and a diagonal matrix D such that A = PDP-¹. Consider the matrix A= 5 0 and its characteristic polynomial (+1)' (1-4)
Now, consider the following theorem: A is diagonalizable if and only if A= PDP-¹, where D is a diagonal matrix and p is an invertible matrix, here the column of p are a basis for R consisting of eigenvectors of A and the diagonal entries of D are the eigenvalues corresponding to the respective columns of p. Therefore, by the above theorem, the invertible matrix P and a diagonal matrix D such that A = PDP-¹ is shown below. P -1 -110 1 0 00 0 1 01 0 0 10 and D= -1 0 0 0 0 -1 00 0 0 -1 0 0 0 0 4 such that A= PDP¹.
Thanks!
- I Just Want To Know How D Is Calculated Thanks 1 (16.24 KiB) Viewed 36 times
- I Just Want To Know How D Is Calculated Thanks 2 (27.68 KiB) Viewed 36 times
Now, consider the following theorem: A is diagonalizable if and only if A= PDP-¹, where D is a diagonal matrix and p is an invertible matrix, here the column of p are a basis for R consisting of eigenvectors of A and the diagonal entries of D are the eigenvalues corresponding to the respective columns of p. Therefore, by the above theorem, the invertible matrix P and a diagonal matrix D such that A = PDP-¹ is shown below. P -1 -110 1 0 00 0 1 01 0 0 10 and D= -1 0 0 0 0 -1 00 0 0 -1 0 0 0 0 4 such that A= PDP¹.