Reputation
10,468
Top tag
Next privilege 15,000 Rep.
Protect questions
Badges
1 11 27
Newest
 Refiner
Impact
~145k people reached

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 $F_Y(y)$?
Aug
11
comment How to show vectors are linearly independent?
@brotherkase What does it mean for $\vec{u}, \vec{v}, \vec{w}$ to be linearly dependent? Use the definition to show the relationship in the answer for some non-zero real numbers $a$ and $b$. Then, compute $$A \vec{u} = A \left(a \vec{v} + b\vec{w}\right)$$ and simplify this expression using the relationship you posted in your answer.
Aug
11
comment Intersection of Collection of Sets
I don't think you mean $A \in S$ -- after all, $S$ is an interval, $A$ is a subset, i.e. $A \subseteq S$ but not $A \in S$...
Aug
11
revised How to show vectors are linearly independent?
vector marks
Aug
11
answered How to show vectors are linearly independent?
Aug
11
revised How to show that $e^{-x}$ tends to $0$ when $x\to \infty$ if $e^{-x}$ is defined as the power series.
added 5 characters in body
Aug
11
revised Simplifying a (approximation) recurrence relation.
added 29 characters in body
Aug
9
comment How do I compute such theoretical expectations?
What is the structure of the graph on which the random walk is being performed?
Aug
9
comment Finding standrad deviation $\sigma$
did you check that $1/3$ of the cartons can be reserved fresh for $22+$ days?
Aug
9
answered Solve this trigonometric equation $ \sin2x-\sqrt3\cos2x=2$