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For more information, please see full course syllabus of Linear Algebra
For more information, please see full course syllabus of Linear Algebra
Linear Algebra Diagonalization of Symmetric Matrices
Lecture Description
We’ve talked about similar matrices, identity matrices, and now we’re going to introduce symmetric matrices. Like the matrices introduced before, symmetric matrices have a special property about them, and that is that the matrix is equal to its transpose. This will complete the theorem introduced last time where the eigenvalues of a matrix can produce a diagonal matrix, where the original matrix has to be a symmetric matrix. After this, we’ll move on to the last subject in linear algebra.
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7 answers
Last reply by: Professor Hovasapian
Wed May 1, 2013 4:41 AM
Post by Matt C on April 28, 2013
Professor Hovasapian
Sorry to spring all these questions on you in one week, but thursday is my final. My professor gave me a matrix and he said that it was diagonalizable. I went through all the steps and I cannot get it to diagonalize. I have the matrix A= [[2,2,-2], [-1,1,2], [0,1,1]], I write all matrix's in column form. He claims that it is diagonalizable, but I have spent a long time trying to figure this out. Lambda = R.
det(A-RI) = -(R-2)(-1+R)^2. R=2, R=1.
(A-1*I)x=0 and I get [ [1,2,-2], [-1,0,2], [0,1,0]], I then subject that to rref. [[1,0,0], [0,1,0],[.5, .5, 0]]. I only have 1 free variable which means the basis is 1, which is less then k. Is there a way where you can quick check if this matrix is Diagonalizable. Like I said I have spent hours on this and I am getting no where.
1 answer
Last reply by: Professor Hovasapian
Mon Feb 25, 2013 3:03 AM
Post by Tach M on February 24, 2013
if the polynomial equation of a matrix M has real and distinct roots, Does it mean that M is similar to a diagonal matrix????