- #1
mathboy20
- 30
- 0
Hi
Given A an n x n matrix where the columns are the set of standard vectors S = {e1, e2,...e_n} in R^n
These vectors are orthonormal according to the definition since
<e_i, e_j> = 0, i \neq j
<e_i,e_i> = 1
Since the columns of A then they are orthonormal according to the definition, and therefore the matrix A is orthogonal matrix which implies that
A^T A = I <---> A^ (-1) = A^T, and so on.
I need to show that the row vectors of of A are orthonormal too.
Any idears on how?
My own idear is that
Since
A^ (-1) = A^T, then the columns in invertible A become the rows in transposed A, and the these orthonormal according to the definition?
Sincerely Yours
Mathboy20
Given A an n x n matrix where the columns are the set of standard vectors S = {e1, e2,...e_n} in R^n
These vectors are orthonormal according to the definition since
<e_i, e_j> = 0, i \neq j
<e_i,e_i> = 1
Since the columns of A then they are orthonormal according to the definition, and therefore the matrix A is orthogonal matrix which implies that
A^T A = I <---> A^ (-1) = A^T, and so on.
I need to show that the row vectors of of A are orthonormal too.
Any idears on how?
My own idear is that
Since
A^ (-1) = A^T, then the columns in invertible A become the rows in transposed A, and the these orthonormal according to the definition?
Sincerely Yours
Mathboy20