If 35 men take 42 minutes to eat 3,000 apples, how long will 35 men take to eat 80,000 apples? Or, am I confusing the mathematical approach?Read more
If 35 men take 42 minutes to eat 3,000 apples, how long will 35 men take to eat 80,000 apples? Or, am I confusing the mathematical approach?Read more
Prove that if A is an m x n matrix, B is an n x m matrix and m>n, then AB is not invertible. I have a lot of trouble starting this exercise!!!Read more
I have an $ N\times N$ lower triangular matrix $ A$ where $ $ A_{i,j}={\bf x}_i{\bf x}_j^H,\quad i>j$ $ $ $ A_{ii}=1,\quad 1\leq i \leq N,$ $ and $ {\bf x}_i$ is a $ 1\times K$ vector, $ K<M$ . I need to study $ A^{-1}$ . Since the matrix $ A$ is formed fromRead more
I’m having a difficult time finding any theory on an inverse problem I’ve come up against. Let’s say I have an unknown function $ f:[0,1] \rightarrow \mathbb{R}$ , and I know $ \int_{a}^{b} f$ for some collection $ A$ of pairs $ (a,b)\in[0,1]^2$ . I’m looking for pointers to any material that discusses condtions onRead more
Inverse of 1/((sqr(s)*tanh(sqr(s))) any answersRead more
Because I had trouble in finding a reliable source on the internet for the matrix inverse algorithm using Gaussian elimination, I wrote one myself. Matrix.h #ifndef MAT4X4_H #define MAT4X4_H class Mat4x4{ public: float mat4x4[4][4]; Mat4x4(); Mat4x4(const Mat4x4& m); Mat4x4(const float m[4][4]); Mat4x4(float t00, float t01, float t02, float t03 , float t10, float t11, floatRead more
I found some codes in libcxx that claim $ \sin^{-1}{z} = \mathrm{Im} (w) + \mathrm{Re} (w) i $ , where $ w = \sinh^{-1}{(\mathrm{Im} (z) + \mathrm{Re} (z) i)}$ . I couldn’t figure this out and no explanation found by googling. Why this happens? Note: I confirmed this with WolframAlpha: https://www.wolframalpha.com/input/?i=Im(asinh(Im(z)%252BIRe(z)))%252BI%2BRe(asinh(Im(z)%252BI*Re(z)))%253Dasin(z)Read more
I’m currently working through Coding the matrix, though I’m trying to work through it using Haskell rather than Python. One of the exercises has you write a function where you take a list of strings, and then transform them into an inverse index of the words contained in each string, along with the index ofRead more
Let $ D$ be a self-adjoint (in the $ H^0$ -inner product) first-order differential operator on a manifold $ M$ , where $ H^i$ stands for the $ i$ -th Sobolev space on $ M$ . Then $ D$ extends to a bounded operator $ H^{i+1}\rightarrow H^{i}$ for each $ i\geq 0$ , self-adjoint inRead more
Suppose that $ G$ is a finite group, $ M$ is a right $ G$ -set and $ N$ is a left $ G$ -set. Then we have a simplicial set $ B(M,G,N)$ whose $ n$ -simplicies are $ M \times G^n \times N$ . Now suppose that $ H \subseteq G$ is a subgroup.Read more