Consider the basis b = {(1,1,0),(1,0,-1),(2,1,0)} for R^3.
which of the following matrices A =[T]bb define symmetric mappings of R^3?
1 1 0
1 1 0
0 0 1
2 0 0
0 2 0
0 0 2
-1 1 2
1 4 0
2 0 1
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Consider the basis b = {(1,1,0),(1,0,-1),(2,1,0)} for R^3.
which of the following matrices A =[T]bb define symmetric mappings of R^3?
1 1 0
1 1 0
0 0 1
2 0 0
0 2 0
0 0 2
-1 1 2
1 4 0
2 0 1
Hey jackGee.
Just to be clear, can you give a definition of symmetric mapping in mathematical form?
Let T : V -----> V be any linear mapping and a={v1,.....,vn} be any orthonormal basis of V
then the matrix A is symmetric iff <T(x),y> = < x ,T(y)> for x,y belong in V
I'm confused by the given basis b because usually I would find a set of eigenvectors and then use it to find an orthonormal basis
then show A is diagonalizable
For these examples, can you just show whether the condition holds by evaluating each example? (In other words, evaluate T(x), T(y) and the inner products given an x, y from the basis corresponding to V)?
so I have to show <Ax,y> = <x ,Ay> where x and y are eigenvectors?
.
Personally I'm wondering if you are dealing with an inner product with the following properties:
http://linear.axler.net/Chapter7.pdf
