MHB Show that in every set p2 with more than three vectors is linearly dependent.

delgeezee
Messages
12
Reaction score
0
i know S = { $$1 , x, x^2$$} is linearly dependent set for p2. where $$(a_0, a_1, a_2) = (0,0,0) $$
I wanted to use the Wronskian on { $$1 , x, x^2, x^3$$} , but as I understand, it only proves linear independence and not the converse.
 
Physics news on Phys.org
delgeezee said:
i know S = { $$1 , x, x^2$$} is linearly dependent set for p2. where $$(a_0, a_1, a_2) = (0,0,0) $$
I wanted to use the Wronskian on { $$1 , x, x^2, x^3$$} , but as I understand, it only proves linear independence and not the converse.

Hi delgeezee!

Can you elaborate?
For starters, what do you mean by p2?
And how do your $a_i$ tie in?
 

Thread '##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?'

I asked online questions about Proposition 2.1.1: The answer I got is the following: I have some questions about the answer I got. When the person answering says: ##1.## Is the map ##\mathfrak{q}\mapsto \mathfrak{q} A _\mathfrak{p}## from ##A\setminus \mathfrak{p}\to A_\mathfrak{p}##? But I don't understand what the author meant for the rest of the sentence in mathematical notation: ##2.## In the next statement where the author says: How is ##A\to...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
View full post »

Similar threads

I Confused about small detail in rank-nullity theorem
Replies
1
Views
1K
I Proving linear independence of two functions in a vector space
Replies
5
Views
2K
I Wronskian: null space equals the span of independent functions
Replies
23
Views
1K
I S is set of all vectors of form (x,y,z) such that x=y or x =z. Basis?
Replies
5
Views
1K
I Row space, Column space, Null space & Left null space
Replies
8
Views
3K
MHB Basis for set of solutions for linear equation
Replies
6
Views
2K
I Proving a set is linearly independant
Replies
5
Views
2K
MHB 12.6 linearly dependent or linearly independent?
Replies
3
Views
2K
I Uniqueness of reduced row echelon form (proof verification)
Replies
4
Views
1K
MHB Are These Vectors Linearly Dependent?
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top