Understanding Change of Basis Vector: What it is and How to Use It

[shounakbhatta]

Hello,

I am doing calculation on change of basis vector.

But I am unable to understand why we do it. I mean to say what is the use of it and where in physics or maths it is used.

Can anybody please explain it?

 

[Mark44]

Hello,

I am doing calculation on change of basis vector.

But I am unable to understand why we do it. I mean to say what is the use of it and where in physics or maths it is used.

Can anybody please explain it?

Changing the basis has several applications, including the diagonalization of matrices, which can be used to solve systems of linear differential equations.

 

[Number Nine]

It's also used very frequently in statistics; given a high dimensional data set, we can construct a new basis set so that most of the variability in the data lies within a few dimensions, allowing us to reduce the dimension of the data without substantially reducing its information content.