# 10. Change of bases

In Section 6.6, we saw that linear operators on an n-dimensional vector space are in one-to-one correspondence with \(n \times n\) matrices. This correspondence, however, depends upon the choice of basis for the vector space. In this chapter we address the question of how the matrix for a linear operator changes if we change from one orthonormal basis to another.

### Contributors

- Isaiah Lankham, Mathematics Department at UC Davis
- Bruno Nachtergaele, Mathematics Department at UC Davis
- Anne Schilling, Mathematics Department at UC Davis

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