2
votes
2answers
45 views

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 ...
0
votes
1answer
26 views

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 $\lVert \mathbf M\cdot \hat v\lVert \leq 1$ ...
1
vote
1answer
22 views

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 ...
0
votes
0answers
15 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 ...
2
votes
2answers
72 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 ...
3
votes
3answers
70 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 ...
0
votes
0answers
47 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: $X⊗X$ $X⊗X⊗X$ $X⊗X⊗X⊗X$ Where $X$ is a matrix? What ...
0
votes
1answer
3k 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... ...
0
votes
1answer
118 views

Kronecker 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.