Imagine I have an arbitrary vector v in RR^n and say it can be represented as v=(v_1,...,v_n)^T where it's understood that the indexes are in increasing order. Imagine now the vector u in RR^(n-1) obtained by simply removing entry with index i of v. What's the best (and most "economic") way to represent such vector? My idea was to simply interpret the vector as a sequence and write u={v_j}_(j != i)^T but I'm not sure whether this is correct and/or there is a better way of writing it. Any ideas?

Makayla Eaton

Makayla Eaton

Answered question

2022-08-11

Imagine I have an arbitrary vector v R n and say it can be represented as
v = ( v 1 , . . . , v n ) T
where it's understood that the indexes are in increasing order. Imagine now the vector u R n 1 obtained by simply removing entry with index i of v. What's the best (and most "economic") way to represent such vector? My idea was to simply interpret the vector as a sequence and write
u = { v j } j i T
but I'm not sure whether this is correct and/or there is a better way of writing it.

Answer & Explanation

pokajalaq1

pokajalaq1

Beginner2022-08-12Added 18 answers

If without writing any components perhaps for v R n you could write u = v / e i R n 1 , as a ''qoutient'', where e i is the i-th standard basis vector in R n . I hope you know quotient spaces.
In some textbooks hats indicate the omission of elements
R n / span { e i } R n 1 v / e i = ( v 1 , , v i ^ , , v n ) T = ( v 1 , , v i 1 , v i + 1 , , v n ) T
darcybabe98ub

darcybabe98ub

Beginner2022-08-13Added 6 answers

If you need it a lot in one text, I think defining an ad hoc notation could be useful. For example, I would consider using something simple like v ( i ) , v i , or something similar. Otherwise, the other answer already give the standard notations I can think of.

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