I have a question about the invertibility of a linear operator T.(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Linear operator

**Physics Forums | Science Articles, Homework Help, Discussion**