Proving the trace of a transformation is independent of the basis chosen
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Proving the trace of a transformation is independent of the basis chosen

How would you prove the trace of a transformation from V to V (where V is finite dimensional) is independent of the basis chosen?

Published: Aug 19, 2026

Why are certain PDE called
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Why are certain PDE called "elliptic", "hyperbolic", or "parabolic"?

Why are the Partial Differential Equations so named? i.e, elliptical, hyperbolic, and parabolic. I do know the condition at which a general second order p...

Published: Aug 19, 2026

How do I find a perpendicular line from an equation in general form?
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How do I find a perpendicular line from an equation in general form?

Suppose I have the line $ax + bx + c = 0$. How do I find the values of $j$, $k$, and $l$ for the perpendicular line $jx + kx + l = 0$? Where the two lines...

Published: Aug 19, 2026

Projection Formula
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Projection Formula

Does someone know if in the problem the projection of x onto U is defined like that : $x_u = \displaystyle \frac{\langle x,u\rangle}{u. u}$ $u$ Problem: L...

Published: Aug 19, 2026

Probability of event occurring multiple times
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Probability of event occurring multiple times

I'm trying to calculate the probability of exactly $8$ identical independent events occurring if each has a $25\%$ chance of occurring. To simplify, ...

Published: Aug 19, 2026

Lines rotation - problem
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Lines rotation - problem

Given $3$ infinite lines $L_1$, $L_2$, $L_3$ in $R^3$ ($3D$ space), each line is represented by two $3D$ points, the line $L_1$ is rotating around the axi...

Published: Aug 19, 2026

Bounded Variation is Bounded
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Bounded Variation is Bounded

Let $f:[a,b]\to \mathbb{R}$ and let $D=\{x_o,x_1,...,x_n\}$ be a division of $[a,b]$. We say that $f$ is of bounded variation on $[a,b]$ if $\displaystyle...

Published: Aug 19, 2026

Find the limit: $\lim\limits_{x\to1}\dfrac{x^{1/5}-1}{x^{1/3}-1}$
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Find the limit: $\lim\limits_{x\to1}\dfrac{x^{1/5}-1}{x^{1/3}-1}$

Find the limit of $$\lim_{x\to 1}\frac{x^{1/5}-1}{x^{1/3}-1}$$ How should I approach it? I tried to use L'Hopital's Rule but it's just keep...

Published: Aug 19, 2026

Given the lenght of the hypotenus and the sum of the legs find the area of right triangle
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Given the lenght of the hypotenus and the sum of the legs find the area of right triangle

Given: right-angled $\triangle ABC$, the length of the hypotenuse $c = 5$ and the sum of the legs $a+b = 6$. Find the area of the triangle. I tried creati...

Published: Aug 19, 2026

Can someone explain the ABC conjecture to me?
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Can someone explain the ABC conjecture to me?

I am an undergrad and I know that the conjecture may have been proven recently. But in reading about it, I am entirely confused as to what it means and wh...

Published: Aug 19, 2026

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