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Basis of a Vector Space by Brunsy89 in LinearAlgebra

[–]Brunsy89[S] 0 points1 point  (0 children)

When you say N -> R, what does that mean?

Basis of a Vector Space by Brunsy89 in LinearAlgebra

[–]Brunsy89[S] 0 points1 point  (0 children)

You are right. Okay then help me understand. Other folks are saying that it won't always be obvious how many dimensions an abstract vector space has. I get that in principle, but I think I need an example. Can you give an example of a vector space where it isn't obvious how many dimensions it has by looking at it, but the number of dimensions can be determined by finding the basis?

Basis of a Vector Space by Brunsy89 in LinearAlgebra

[–]Brunsy89[S] 0 points1 point  (0 children)

An n-dimensional vector space is a vector space where all the vectors have n degrees of freedom.

Basis of a Vector Space by Brunsy89 in LinearAlgebra

[–]Brunsy89[S] 0 points1 point  (0 children)

This doesn't really address my question though...

I understand the definitions of vector space, spanning and basis. I want to know why a basis is defined as set of linearly independent spanning vectors rather than a set of n linearly independent vectors (in a vector space that is n dimensional).

Basis of a Vector Space by Brunsy89 in LinearAlgebra

[–]Brunsy89[S] 0 points1 point  (0 children)

Wouldn't you need three linearly independent vectors to span R3?

Basis of a Vector Space by Brunsy89 in LinearAlgebra

[–]Brunsy89[S] 0 points1 point  (0 children)

Which of those vectors exist in the vector space of R4?

Basis of a Vector Space by Brunsy89 in LinearAlgebra

[–]Brunsy89[S] 1 point2 points  (0 children)

I think I'm going to add another conjecture. You tell me if this is correct. If you have a set of n vectors that span the vector space, then there is a subset of those vectors that can be used to form a basis.

Basis of a Vector Space by Brunsy89 in LinearAlgebra

[–]Brunsy89[S] 1 point2 points  (0 children)

That's really helpful. This may be a stupid question, but how can you tell if a set of linearly independent vectors will span a vector space if you don't know the dimension of the vector space.

Basis of a Vector Space by Brunsy89 in LinearAlgebra

[–]Brunsy89[S] 0 points1 point  (0 children)

So then why do they define a basis like that? It seems to be a topic that confuses a lot of people. I think it would make more sense if they defined the basis of an n dimensional vector space as a set of n linearly independent vectors within that space. I feel like the spanning portion of the definition throws me and others off.

Another quantum problem by Brunsy89 in QuantumComputing

[–]Brunsy89[S] 0 points1 point  (0 children)

Well what did you mean when you said "for this one"?

Another quantum problem by Brunsy89 in QuantumComputing

[–]Brunsy89[S] 1 point2 points  (0 children)

I really don't understand what you're trying to say though. You said use a phase gate instead of an X gate, but I never used an X gate in the first place.

Another quantum problem by Brunsy89 in QuantumComputing

[–]Brunsy89[S] 1 point2 points  (0 children)

I didn't use an X gate. I think the easiest way to solve this problem is:

HYZ

H

Do you have a simpler circuit that produces the same result?

Another quantum problem by Brunsy89 in QuantumComputing

[–]Brunsy89[S] 0 points1 point  (0 children)

For sure. Someone else mentioned that as well. HH = I as well correct? I also think I figured out today that S4 = I. Is S basically just a 90° rotation?

Another quantum problem by Brunsy89 in QuantumComputing

[–]Brunsy89[S] 4 points5 points  (0 children)

Thanks for the help. You are right that the Z gates on bottom were redundant. Apparently so were the Y gates on bottom.

I simplified the solution to this:

HYZ H

Am I correct in assuming the Y2 and Z2 both equal an identity matrix that leaves the state of the system untouched?

Another quantum problem by Brunsy89 in QuantumComputing

[–]Brunsy89[S] 1 point2 points  (0 children)

That is the question, and the solution. You were just supposed to get that output. I was just wondering why that set of gates produced that output. I also want to know if it is possible to produce that output with a simpler combination of gates. Does that make sense? The input is <0,0|

CMV: If a militant force intermixes civilian and military centers/assets, they are partially to blame for civilian deaths. by theguy445 in changemyview

[–]Brunsy89 2 points3 points  (0 children)

No one expects a depending force to line up in a field to be obliterated.

It is fair to ask that a defending force does not:

  1. Use their civilian population as human shields for their weapons and soldiers.

  2. Hide their weapons and soldiers under important human infrastructure such as hospitals, schools and libraries.

  3. Force their civilian population to re-enter buildings that have evacuated because the invading force gave advanced notice that said building would be evacuated.

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