- #1
typhoonss821
- 14
- 1
I have a question about the invertibility of a linear operator T.
In Friedberg's book, Theorem 6.18 (c) claims that if B is an orthonormal basis for a finite-dimensional inner product space V, then T(B) is an orthonromal basis for V.
I don't understand the proof, I think the book only prove that T(B) is orthonormal.
If T is not one-to-one, why T(B) is also linear independent?
In Friedberg's book, Theorem 6.18 (c) claims that if B is an orthonormal basis for a finite-dimensional inner product space V, then T(B) is an orthonromal basis for V.
I don't understand the proof, I think the book only prove that T(B) is orthonormal.
If T is not one-to-one, why T(B) is also linear independent?