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Aug
18
awarded  Custodian
Aug
18
revised Proof that applying the difference operator to a $d$-degree polynomial $d$ times yields $d!a_d$
edited tags; edited title
Aug
18
reviewed Leave Open Show that the propositions r → s and ¬r ∨ s are equivalent
Aug
18
reviewed No Action Needed Prove by induction $4^n > n^2$ for $n \geq 1$
Aug
18
reviewed No Action Needed Limiting how often an element can repeat
Aug
18
comment Integrating unit impulse function
@Clayton this is using Stjeltjes interpretation of the integral, allowing to take care of discrete points with a weight...
Aug
18
comment Integrating unit impulse function
Look at en.wikipedia.org/wiki/Dirac_delta_function
Aug
18
comment Integrating unit impulse function
You likely mean $\delta(t) = 0$ for $t \ne 0$. Note that (A) follows from (B) with $f(t) \equiv 1 \forall t$.
Aug
17
answered Vector spaces $V=-V$
Aug
11
comment Show that if λ is an eigenvalue of a projection matrix P, then λ = 1 or λ = 0
+1, short and elegant
Aug
11
comment How to show vectors are linearly independent?
@Kaster done, please look again...
Aug
11
revised How to show vectors are linearly independent?
added 290 characters in body
Aug
11
comment How to show vectors are linearly independent?
@Kaster You're right, but this case is different since they are eigenvalues of the same matrix. I will change the answer in a sec
Aug
11
revised Show that if λ is an eigenvalue of a projection matrix P, then λ = 1 or λ = 0
added 51 characters in body
Aug
11
revised find the supremum and infimum of $E =\{x \in \mathbb{R} : -1/n \le x \le 1-1/n\}$
edited title
Aug
11
comment How to show vectors are linearly independent?
@Kaster I did not use the full definition, what I used is a direct consequence of the definition...
Aug
11
comment How to show vectors are linearly independent?
@Kaster yes. If $\vec{v}, \vec{w}$ are LD, so is any other collection of vectors with these included. For your case, let $a = 0, b = -2$ and $c = 1$ and note that $$a\vec{u} + b \vec{v} + c \vec{w} = \vec{0}.$$ The constants in the definition of LD cannot be all zero, but some of them can be zero at will.
Aug
11
comment What is CDF $F_X(x) $ and $F_Y(y)$?
@Math-fun thank you very much, appreciate it, totally overlooked
Aug
11
comment How to show vectors are linearly independent?
@Kaster not sure this is intended for me. Add the brotherkase tag if not. Certainly, $\vec{v}, \vec{w}$ are linearly dependent and suitable constant are easily found.
Aug
11
answered What is CDF $F_X(x) $ and $F_Y(y)$?