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Spanning set is closed.
Suppose $\{e_1,e_2,\ldots,e_n\}$ is an orthonormal set in $\mathscr{H}$ (Hilbert space) and define $$M \equiv \operatorname{span}\{e_1,e_2,\ldots,e_n\}.$$...
Apr 16, 2026
Archive: News
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Show that rank of a matrix is unique
I know that row rank of a matrix is the number of row vectors that span row space of the matrix. Column rank can be similarly defined. I also know that ro...
Apr 16, 2026
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Find the volume of the region outside cone and inside sphere.
Find the volume of region outside the cone $\varphi = \frac{\pi}{4}$ and inside the sphere $\rho =4cos(\varphi)$. Solution Attempt: I can visualize the su...
Apr 16, 2026
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Derivative of Integral with variable bounds
I was testing my calculus knowledge when I found an example final exam from UCIrvine: http://www.math.uci.edu/sites/math.uci.edu/files/2B_final_samp1.pdf ...
Apr 16, 2026
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Definition of a finite series
I know that the definition of an infinite series is the limit as $n \to \infty$ of its partial sums. $$\underbrace{\sum_{n=0}^{\infty} \ \ a_n}_\text{Infi...
Apr 16, 2026
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What's the probability a random game of Connect 4 ends in a draw?
On a standard Connect-$4$ board ($7$ columns & $6$ rows), if two players take turns making moves by selecting an available column uniformly at random,...
Apr 16, 2026
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Closed form of $\cot x=x$
I plotted the graphs of $y=\cot x$ and $y=x$. Its clear that they have infinite intersections. I tried to solve for the first root but it doesn't see...
Apr 16, 2026
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Is there a general form for the derivative of a matrix to a power?
Let $S:Mat(2,2) \rightarrow Mat(2,2)$ be the squaring map $S(A)=A^2$ then $[DS(A)]B=AB+BA$. I was wondering if there was a general form for this solution ...
Apr 16, 2026
news
Finding the volume using cylindrical shells about the x-axis
So I have spent about a hour on this problem and figured it was time to ask for some advice. The problem is to find the volume using cylindrical shells by...
Apr 16, 2026
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What is parameterization?
I am struggling with the concept of parameterizing curves. I am not even sure if I know what it means so I tried to look some things up. On Wikipedia it s...
Apr 16, 2026
