Tobias Ali

2021-02-19

To explain^ Why the beta-coordinate vectors of $\beta ={b}_{1},...,{b}_{n}$

are the columns${e}_{1},...,{e}_{n}$

of the$n\times n$ identity matrix.

are the columns

of the

Benedict

Skilled2021-02-20Added 108 answers

Consider a vector x in V such that,

The coordinates of x relative to basis

also called beta-coordinates of x are given by,

Since

Thus, the vectors

Therefore, if any vector

That is, an arbitrary vector

can be written as

Here, k varies from 1 to n.

Thus, the beta-coordinates of

in this case are

The matrix formed by these beta-coordinates is

That is, beta-coordinate vectors of

are the columns

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