# Tagged Questions

6k views

### Why learn to solve differential equations when computers can do it?

I'm getting started learning engineering math. I'm really interested in physics especially quantum mechanics, and I'm coming from a strong CS background. One question is haunting me. Why do I need ...
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### How to find a basis of an image of a linear transformation?

I apologize for asking a question though there are pretty much questions on math.stackexchange with the same title, but the answers on them are still not clear for me. I have this linear operator: ...
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### Suggestion for a book on Linear Algebra [duplicate]

Please suggest a Linear Algebra book with an introduction and rigorous theory (description) on Eigenvectors , eigen-values , Cayley-Hamilton theorem , Diagonalisation of matrices ; Quadratic forms ( ...
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### Inner product of functions as integration

I am trying to teach my self some linear algebra in preparation for a module in machine learning. I am using Gilbert Strang's text Introduction to Linear Algebra and am having some difficulties. My ...
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### Volume of parallelepiped gets smaller when using projection vectors

Given a Euclidean Space R and a subspace R' (of dimension $\geq$m), consider vectors $x_1,...,x_m \in$**R**, and let $V[x_1,...,x_m]$ mean the volume of an m-dimensional parallelepiped formed by those ...
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### Generator Matrix

I have a C in $F_2^6$ $(x_1,x_2,x_3,x_4) \to (x_1,x_2,x_3,x_4,x_1+x_2,x_3+x_4)$ for $x = (1,0,1,1)$ i get $c = (1,0,1,1,1,0)$ we know that $$c = G . x$$ G is the Generator Matrix in the solution ...
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### Area preserving transformation in a higher dimensional space is unitary.

In $\mathbb{R}^3$, a linear operator $Q:\mathbb{R}^3 \to \mathbb{R}^3$ preserves the area of parallelograms: that is, given $x,y\in \mathbb{R}^3$, the area of a parallelogram formed by $x$ and $y$ is ...
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### Gauss-Jordan Method

I keep getting the wrong set of solutions can someone help me. I know that when using the Gauss-Jordan method, the rules that I must follow can be applied in a variety of different procedures then why ...
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### symmetric normalized Graph Laplacian and symmetric normalized Adjacency matrix share the same eigenvalue

I am trying to show that the symmetric normalized Graph Laplacian and symmetric normalized Adjacency matrix share the same eigenvalues ($\lambda_i$ and $1 - \lambda_i$ for i=1 to n. $\lambda$ is an ...
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### Some aspects of inner products in $\mathbb R^3$

I read several descriptions about inner products recently due to an exercise (here it is no longer active so I like to ask again). I am still very confused about this concept. Any clarification will ...
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### On the canonical isomorphism between $V$ and $V^{**}$

I am trying to understand more about the Bidualspace (or double dual space). The whole idea is that $V$ and $V^{**}$ are canonically isomorphic to one another, which means that they are isomorphic ...
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I have function $\sigma(u,v)=(f(u,v),g(u,v),h(u,v))$ s.t. $\sigma_u$ x $\sigma_v\neq(0,0,0)$ (cross-product) also, there is the $3\times 2$ matrix : $$... 2answers 49 views ### Example- l_p norm space$$||x||= {[{\sum _{i=1}^\infty |x_i|^p}]}^{1/p}$$Is a norm on l_p space :- space of all sequences made of scalars from \mathfrak C(filed of complex numbers). To prove that above is norm on l_p ... 2answers 33 views ### Showing that two Matrices are not similar over GL_n(\mathbb{F}_2) Problem: Show that$$ \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}, \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} $$Are not similar over GL_n ( \mathbb{F}_2) Note: We write ... 1answer 75 views ### F,G \in \text{End} (V) share the same eigenvalues for F \circ G and G \circ F Problem: Let V be a finite dimensional Vector Space over a field \mathbb{F} and F,G \in \text{End}(V)  Show that F \circ G and G \circ F have the same Eigenvalues \lambda My ... 2answers 74 views ### Linear Algebra Self Study I'm currently a high school student with a love for math. I have taken Plane and Coordinate Geometry, both Algebra I and II, Trigonometry, and am halfway done with Calc A. I want to major in quantum ... 1answer 45 views ### Pre requisites of linear algebra I want to learn abstract linear algebra. Do I require the knowledge of discrete mathematics before I start? I have the impression that abstract maths and their proofs can be understood easily by the ... 4answers 176 views ### \hom(V,W) is canonic isomorph to \hom(W^*, V^*) Introduction My Semester just started and we have a new Professor for Linear Algebra II (replacing our former Professor). Apparently we are behind our schedule and thus we only had a brief ... 1answer 18 views ### Question regarding dimension of linear transformation. I saw in an exercise that if T is a linear transformation T: V\rightarrow W and T_2: W\rightarrow Z and T_1: X\rightarrow V are invertible then the rank of the composition doesn't change. So, ... 1answer 61 views ### Checking if systems of linear equations are equivalent I'm going through Hoffman and Kunze's Linear Algebra on my own and can't for the life of me figure out part of Exercise 3 of Section 1.2: Are the following two systems of linear equations equivalent? ... 1answer 56 views ### Show that T\neq{T^*} Let V=P_2(\mathbb{R}), T\in \mathcal{L}(P_2(\mathbb{R})), where T(p)=(a_1x). Make V an inner product space by defining$$\langle p,q\rangle=\int_0^1{p(x)q(x)\,dx}$$So I calculate$$\langle ...
Hi everyone is my first time reading about dual spaces and in one part of the notes that I read, says: The dual of the quotient space $V/U$ is naturally a subspace of $V$, namely the annihilators of ...