# Tagged Questions

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### What is the dot product of two or three vectors graphically or visually?

I don't understand what the dot product actually is. I understand when and where to use it, but when it comes to proving things with it, I don't really grasp what it actually is making it difficult ...
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### How do I do the math necessary to make these five matrices multiplied together equal the result shown?

I'm currently studying the math involved with rotating vertices around an arbitrary axis in 3D space. For this, I have found the following page to be very helpful: ...
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### Matrix-Vector Product

Suppose I have the expression $\lVert\mathbf B \cdot\hat n\lVert=1$, where $\mathbf B$ is a matrix and $\hat n$ is a unit vector (both can have any dimensions, as long as they are compatible). What ...
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### Restrictions on a Matrix-Vector product

Suppose I have a $m\times n$ matrix $\mathbf M$, and a unit vector $\hat v$, of dimension $n$. What restrictions do I need to apply to $\mathbf M$ so that $\lVert \mathbf M\cdot \hat v\lVert \leq 1$ ...
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 ... 0answers 16 views ### Distribution of Matrix and Vector products Given the following expression: $$\vec w = (\mathbf M\cdot\vec u) + (\vec v\cdot\vec u)$$ Where$\mathbf M$is a matrix of dimension$n\times m$,$\vec v$and$\vec u$are vectors of dimension ... 2answers 73 views ### When can we write the square of a matrix as the product of the matrix and its transpose? I often see something like$(A - B)^2$being written as$(A - B)(A - B)^T$. Here$A$and$B$are two matrices. I can see that this is possible when$A$and$B$are scalars (i.e) single element ... 3answers 88 views ### Vector multiplication. Difference between scaler and dot product? We just started a new class where the first topic is briefly talking about vectors and vector multiplication. All tying this into neural networks. I am a bit behind with the understanding of what the ... 0answers 64 views ### Notation for Kronecker product of a matrix and itself? What is the notation for the Kronecker product of a matrix and itself? In other words, is there a short-hand way I can express the following:$X⊗XX⊗X⊗XX⊗X⊗X⊗X$Where$X$is a matrix? What ... 1answer 4k views ### Magnitude of a Matrix? Consider a vector V. The magnitude of this vector (if it describes a position in euclidean space) = distance from the origin is simply:$(V^TV)^{1/2} \$ aka the square root of the dot product... ...
Is this right $$\mathbf{A}\left(\mathbf{B}\otimes\mathbf{C}\right)\mathbf{D}=\left(\mathbf{A}\mathbf{B}\mathbf{D}\otimes\mathbf{C}\right)$$ Thanks in advance for your help.