FIStheorem 2.15 - 2

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[pastel torrent]

why is the first sentnce of a correct?

shoudn't it be the coordinate vector of LA(ej)

[valid mist]

per definition of L_A

the jth column is the image of the jth basis vector

i.e Aej

[hollow jolt]

@pastel torrent

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[pastel torrent]

I think it should be the coordinate vector of that

[valid mist]

it already is a coordinate vector

A is applied to an n x 1 matrix

resulting in an m x 1 matrix

i.e, a vector

[pastel torrent]

Is it because beta and gamma are standard ordered basis

[valid mist]

they can be any bases

you would simply get different coordinates if that were the case

[pastel torrent]

Why is that already a coordinate vector?

[valid mist]

Aej is an m x 1 matrix by definition

i.e a vector

it's written right there, this is not a novel you read without stop, think about what the thing is saying

[pastel torrent]

I know it’s a vector, but a vector is not always a coordinate vector

A matrix is also a vector

[valid mist]

it is also the image of the jth basis vector

or more precisely, the coordinate vector of the image

[valid mist]

every vector in F^m or F^n is a coordinate vector

that's by definition of basis

[pastel torrent]

It’s the coordinate vector of standard basis?

, rotate

[pastel torrent]

I have a proof for (e) (the first line)

Also in f, what does I f^n mean?

Shouldn’t it be a natural number like In?