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Feb
23
comment Prove $\sin^2\theta + \cos^2\theta = 1$
@Sami Ben Romdhane How do we get last implication? Where did it come from?
Feb
22
answered Find a vector that spans the given set
Feb
22
comment Find a vector that spans the given set
-2,5,3 is a vector from H. I think the answer 1,3,2 is incorrect. How do we get -2,5,3 from 1,3,2?
Feb
22
comment Basis for a vectorspace
The condition given, $\text{dim}(U)=2$, implies they exist
Feb
22
comment Basis for a vectorspace
condition $\text{dim}(U)=2$ implies that $U$ is spanned by two independent vectors from $\mathbb{R}^3$. Task is to show them.
Feb
22
comment Basis for a vectorspace
are you sure this is written as you said?
Dec
20
awarded  Constituent
Dec
13
comment How prove this rank identity $r(A)=r(B)$
Thank you for correcting my mistaken answer and giving us this more structural proof
Dec
8
awarded  Caucus
Dec
7
revised Finding a basis for two subspaces of $\mathbb {R}^4$
added 324 characters in body
Dec
7
answered Finding a basis for two subspaces of $\mathbb {R}^4$
Dec
7
awarded  Yearling
Dec
7
revised Prove that if $f'(x)\gt 0$ , then the function is increasing, and if $f'(x)\lt 0 $ then the function is decreasing.
deleted 60 characters in body
Nov
2
answered Prove that if $f'(x)\gt 0$ , then the function is increasing, and if $f'(x)\lt 0 $ then the function is decreasing.
Nov
2
answered Linear Independence in R^n
Nov
2
revised Prove an implication about quadratic form definiteness
added 32 characters in body
Oct
7
comment Prove an implication about quadratic form definiteness
@Daniel thank you very much
Oct
7
comment Prove an implication about quadratic form definiteness
@Daniel yes, that's it, you can post this as an answer, but I think we should first show that result is true for n=2, because for n=1 it is trivial. Then we show that it is true for any n, based on fact that n-1 is positive definite. The result for n comes always from the fact that $\det A^TA = ( \det A )^2>0$
Oct
7
comment Prove an implication about quadratic form definiteness
We want to prove => in statement: quadratic form $q$ over an $n$-dimensional real linear space $V$ is positive definite $\iff$ all main minors $\Delta_1, \Delta_2, ..., \Delta_n > 0$
Oct
7
comment Prove an implication about quadratic form definiteness
@Daniel "Thus, by induction on the dimension its main minors are positive." - but the fact that if q is positive then minors are positive is what we have to PROVE now