Questions tagged [vectors]

Use this tag for questions and problems involving vectors, e.g., in an Euclidean plane or space. More abstract questions, might better be tagged vector-spaces, linear-algebra, etc.

7,492 questions
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Row vector vs. Column vector

I'm a student in an elementary linear algebra course. Without bashing on my professor, I must say that s/he is very poor at answering questions, often not addressing the question itself. Throughout ...
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What does the symbol nabla indicate?

First up, this question differs from the other ones on this site as I would like to know the isolated meaning of nabla if that makes sense. Meanwhile, other questions might ask what it means in ...
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Difference between sum and direct sum

What is the difference between sum of two vectors and direct sum of two vector subspaces? My textbook is confusing about it. Any help would be appreciated. Thanks in advance!
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What is vector division?

My question is: We have addition, subtraction and muliplication of vectors. Why cannot we define vector division? What is division of vectors?
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What equation produces this curve?

I'm working on an engineering project, and I'd like to be able to input an equation into my CAD software, rather than drawing a spline. The spline is pretty simple - a gentle curve which begins and ...
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3rd type of vector multiplication beside dot/cross product?

I was reading up on how to find the square root of i , and I learned that multiplication of complex numbers could be viewed geometrically by viewing the complex numbers as coordinates on the complex ...
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How to define the inverse of a vector?

Most physical situations in mechanics can be modeled using a combination of derivatives - specifically, derivatives of position: velocity and acceleration. But physical situations can also be modeled ...
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Is zero a scalar?

Is zero considered a scalar? In other words, is $\begin{bmatrix}0\\0\\\end{bmatrix}$ a scalar multiple of $\begin{bmatrix}a\\b\\\end{bmatrix}$ where $a$ and $b$ are real numbers?
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What is the intuition behind the definition of the differential of a function?

What is the intuition behind the definition of a differential of a function in differential geometry? i.e. $$df(p)(v_{p}) =v_{p} (f)(p)$$ where $v_{p} \in T_{p} M$ is a vector in the tangent space to ...
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Set, n-Tuple, Vector and Matrix — links and differences

I know this question has been asked like 1000 times, however all supplied answers were not really satisfying to me. My question concerns the similarities and differences between these mathematical ...
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Why is $v/\|v\|$ not a unit vector?

I have a homework question that is seriously stumping me. It was a true/false statement. The statement is "If $v$ is any vector in an inner product space $V$, then $v/\|v\|$ is a unit vector" ...
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how does the dot product determine similarity?

I want to know how the dot product can determine whether two vectors are similar? I know that the formula $$\cos(\theta) = \frac{u \cdot v }{ ||u||\,||v||}$$ means something, but don't know what.
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Kronecker product and outer product confusion

I have two column vectors: $$u = \left[\matrix{ 1 \cr 2\cr }\right]$$ $$v = \left[\matrix{ 4 \cr 4\cr }\right]$$ I'm trying to ...
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Norm of a Matrix-vector product

Suppose I have vector $\vec x \in \mathbb R^n$ and matrix $\mathbf M$ of dimension $m\times n$. Is there an alternative expression for $\lVert \mathbf M \cdot \vec x \lVert$ that includes \$\lVert \vec ...