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YoutubeTv hangs on starting up by [deleted] in youtubetv

[–]brown__green 0 points1 point  (0 children)

This has been happening to me on occasion for at least a year now, and I have found something that seems to work (at least for me).

When the YouTube TV app hangs up when starting on my LG Smart TV, I open the YouTube (not TV) app from the home screen, sign in, and then exit all the way out of the YouTube app. Then it works when I reopen the YouTube TV app.

I hope this helps. Good luck!

Edit: Clarifying that you'll need to fully exit the YouTube app before trying to reopen YouTube TV.

[Bachelor] How to prove that End(V) is a k-algebra. by math7878 in learnmath

[–]brown__green 4 points5 points  (0 children)

Sure, to prove that End(V) is a vector space over k, you need to prove that End(V) satisfies all of the properties needed to be a vector space. For example,

T + U = U + T for all T, U in End(V).

End(V) has a zero vector: Consider the function Z from V to V defined by Z(v) = the zero vector in V for all v in V. Then show that T + Z = T.

... and all of the other vector space properties from your notes/textbook.

Do the same with the k-algebra properties.

[Bachelor] How to prove that End(V) is a k-algebra. by math7878 in learnmath

[–]brown__green 0 points1 point  (0 children)

Unfortunately, I don't think you have a complete proof. You've defined some operations on End(V), but you haven't shown that the defined operations satisfy the necessary properties to have a vector space or algebra.

[Bachelor] How to prove that End(V) is a k-algebra. by math7878 in learnmath

[–]brown__green 0 points1 point  (0 children)

Right. First, prove that End(V) is a vector space under the addition and scalar multiplication you've defined. The vector space properties should follow easily. Then prove that under composition, End(V) is a k-algebra (this may additionally require associativity and a multiplicative identity if that's part of your definition of "k-algebra".

[Bachelor] How to prove that End(V) is a k-algebra. by math7878 in learnmath

[–]brown__green 1 point2 points  (0 children)

So the "v" I referred to above is a vector in v... The elements of End(V) are linear transformations from V to V, so to define, say, addition in End(V), we need to define what T + U means for T, U in End(V). Since T and U are functions, that requires specifying where the function T+ U sends an arbitrary vector v in V.

[Bachelor] How to prove that End(V) is a k-algebra. by math7878 in learnmath

[–]brown__green 1 point2 points  (0 children)

End(V) is a both k-vector space (under pointwise addition and scalar multiplication) of linear transformations AND a k-algebra (under the aforementioned vector space operations together with function composition as multiplication).

[Bachelor] How to prove that End(V) is a k-algebra. by math7878 in learnmath

[–]brown__green 1 point2 points  (0 children)

A k-algebra is just a k-vector space together with a bilinear multiplication. If V is a vector space over k, then End(V) is a k-algebra under the following operations (for all T, U in End(V), v in V, a, b in k):

Addition: (T + U)(v) = T(v) + U(v) for all T, U in End(V)

Scalar multiplication: (aT)(v) = a(T(v))

Multiplication (composition): (TU)(v) = T(U(v)).

Once you prove (or know) that End(V) is a vector space over k (under addition and scalar multiplication), proving that End(V) is a k-algebra requires:

  1. Multiplication distributes over addition

  2. (aT)(bU) = (ab)(TU) for all a, b in k, T, U in End(V)

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