Conflict of interests results in lies?

  • Thread starter seang
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In summary: However, one thing to keep in mind is that just because two spaces are isomorphic, that doesn't mean they are the same space.
  • #1
seang
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Hello, I am currently studying Electrical Engineering. I have this class where we quickly go over selected math topics which will be oft used in our careers.

I'm also enrolled in Linear Algebra (not matrix algebra. The difference at my school is that Linear Algebra is based much more around proofs and theory, and matrix algebra is more application oriented; I'm not sure if this is the case most places.).

Anyway in my EE class, one of the topics was linear algebra. We basically learned everything we learned in my linear algebra class minus proofs and orthogonality.

So let me get to the point here. There was a true/false question on my EE exam that asked whether R2 was a subspace of R3. The answer accoring to my prof was true. However I remember my linear algebra teacher explaining to us why it wasn't. What's the story? Our linear algebra teacher said something about isomorphism, which we didn't cover in my linear algebra class, so I couldn't really argue much with my EE teacher.

Any clarification?
 
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  • #2
Given a vector space isomorphic to R^3, then there are infinitely many non equal subspaces all isomorphic to R^2 - any choice of two linearly independent vectors will span one. However, there is in one sense no such thing as 'the vector space R^3', or 'the vector space R^2', though we often ignore this fact. The class of real vector spaces of dimension 3 is not even a set. So it is moot to ask 'is R^2 a subspace of R^3'. It is true, and no one can argue with this, that given a vector space of dimension n over a field F, then there are subspaces of dimension m for all 0<=m<=n.
 
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  • #3
If by R^2, you mean a 2-dimensional vector space over R, and by R^3, you mean a 3-dimensional vector space over R, then the correct statement is that R^2 is isomorphic to a subspace of R^3 (one possible isomorphism is mapping all pairs (x, y) to 3-tuples (x, y, 0)), but R^2 is obviously not itself a subspace of R^3, since R^2 consists of 2-tuples and R^3 consists of 3-tuples.
There will be a lot more glossing over of isomorphisms when talking about physics/engineering.
 
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FAQ: Conflict of interests results in lies?

What is a conflict of interest?

A conflict of interest occurs when an individual or organization has competing interests that could potentially influence their decision-making or actions in a particular situation.

How does a conflict of interest lead to lies?

When an individual or organization has a financial or personal interest in a particular outcome, they may be tempted to manipulate or conceal information in order to serve their own interests. This can lead to lies or misinformation being presented as truth.

Can a conflict of interest be avoided?

While it is not always possible to completely avoid conflicts of interest, steps can be taken to minimize their impact. This can include disclosing potential conflicts of interest, recusing oneself from decision-making processes, and seeking independent verification of information.

How can conflicts of interest be identified?

Conflicts of interest can be identified by examining the potential biases or motivations of individuals or organizations involved in a particular decision or situation. This can include looking at financial relationships, personal connections, and past actions or statements.

What are the consequences of conflicts of interest?

Conflicts of interest can have serious consequences, including eroding trust in institutions, compromising the integrity of research or decision-making processes, and leading to legal or ethical violations. It is important for individuals and organizations to actively address and manage conflicts of interest in order to maintain credibility and avoid negative consequences.

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