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Describe command word in questions

  • Thread starter Ted123
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"Describe" command word in questions

I always find it a bit vague when a question tells me to "Describe".

For example "Describe the kernel of [itex]\phi[/itex]". Does this just mean find it?

If you see the word "Hence" it means use the previous result.
 

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  • #2
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I always find it a bit vague when a question tells me to "Describe".

For example "Describe the kernel of [itex]\phi[/itex]". Does this just mean find it?

If you see the word "Hence" it means use the previous result.
What do you mean when you "find" the kernel? "Describe the kernel" suggests to me that you are meant to find a basis for the kernel, and this basis completely characterizes the kernel.

"Hence" means that the next statement follows from the previous statement. I don't see any difference between "hence," "ergo," or "therefor."
 
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Well the question I'm referring to is (in the context of lie algebras but similar for linear algebra): 'describe the kernel of the canonical homomorphism [itex]\phi : \mathfrak{g} \to \mathfrak{g} / \mathfrak{h}[/itex]' defined by [itex]\phi (x)=x+\mathfrak{h}[/itex] for all [itex]x\in\mathfrak{g}[/itex] where [itex]\mathfrak{g}[/itex] is any lie algebra (vector space with some additional properties) and [itex]\mathfrak{h}[/itex] is an ideal (subspace with some additional properties) of [itex]\mathfrak{g}[/itex].

I've found that [itex]\text{Ker}( \phi ) = \mathfrak{h}[/itex] but how would I present a basis?

What I mean by finding the kernel is using the definition [itex]\{ v\in V : \phi v)=0 \}[/itex]
 
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  • #4
33,632
5,287


Well the question I'm referring to is (in the context of lie algebras but similar for linear algebra): 'describe the kernel of the canonical homomorphism [itex]\phi : \mathfrak{g} \to \mathfrak{g} / \mathfrak{h}[/itex]' defined by [itex]\phi (x)=x+\mathfrak{h}[/itex] for all [itex]x\in\mathfrak{g}[/itex] where [itex]\mathfrak{g}[/itex] is any lie algebra (vector space with some additional properties) and [itex]\mathfrak{h}[/itex] is an ideal (subspace with some additional properties) of [itex]\mathfrak{g}[/itex].

I've found that [itex]\text{Ker}( \phi ) = \mathfrak{h}[/itex] but how would I present a basis?
I was thinking vector spaces when you asked the question (and there wasn't any context to let me know you weren't talking about vector spaces).
What I mean by finding the kernel is using the definition [itex]\{ v\in V : \phi v = 0 \}[/itex]
This is just the definition of the kernel, so you haven't really found anything.
 

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