# Physical meaning of orthonormal basis

1. Aug 5, 2010

### LGB

I want to know what orthonormal basis or transformation physically means. Can anyone please explain me with a practical example? I prefer examples as to where it is put to use practically rather than examples with just numbers..

2. Aug 6, 2010

### HallsofIvy

Staff Emeritus
I would think that a "physical" meaning of an orthonormal basis is exactly what it says: a basis in which each basis vector has length 1 and are all perpendicular to each other.

Given any coordinate system in which the coordinate axes cross at right angles, the vectors defined by the coordinates will form an orthonormal basis.

Perhaps I just don't know what you mean by a "physically means". Mathematical concepts can have a number of different physical interpretations. They do not have a specific physical meaning.

3. Aug 6, 2010

### LGB

Thank you HallsofIvy. I just meant the physical interpratation only. I wanna know where it is practically been put to use. Also I need to know about orthonormal matrices used in PCA(Principal Component Analysis). Suppose if am recording some 100 data and I need to eliminate noise and redundancy, am going for PCA. There i have to use orthonormality. The thing is I couldn't visualize wat actually orthonormal transformation does. Need some help on it.