0
votes
0answers
11 views

similarities between two binary matrices

I want to measure the similarities between two matrices A and B. Both A and B contains the feature vectors of sounds and are in binary format. i want to see what is the similarities between these two ...
0
votes
0answers
37 views

Is a set of some $m \times n$ matrices a relation?

A relation between sets $A_i, i = 1, \dots, n$ is defined as a subset of $\prod_i A_i$. Given $m, n \in \mathbb N$, is a set of (some or all) $m \times n$ matrices over $\mathbb R$ considered a ...
1
vote
1answer
50 views

$M_{R^n}$; how to derive $n$ for transitive closure?

When finding the transitive closure of a relation $R$, I convert $R$ into a boolean matrix $M_R$, and find the union between $M_R$ and its powers up to $n$. $$M_{R^*} = M_{R^1} \lor M_{R^2} \lor ...
0
votes
1answer
65 views

Help understanding a theorem on transitivity of a relation

The theorem states this: The relation R on a set A is transitive if and only if $R^n \subseteq R$ for n = 1, 2, 3,... What I'm reading is that the nth power of that set is transitive if the set ...
0
votes
1answer
38 views

In a boolean matrix, what does the $n$ in $M_{R^n}$ represent?

I'm now learning about binary relations. I stumbled upon this question in the book: Given $A = \{1,3,5,6\}$ and $R$ is a relation over $A$, whose matrix is defined by $$\begin{pmatrix} 0 ...
0
votes
1answer
290 views

Matrix of a relation on a set

If I have a Matrix $A=\begin{bmatrix} 0&0&0\\ 0 & 0 & 0 \\0&0&0\end{bmatrix}$ why is this both symmetric and anti-symmetric? If I had a Matrix $B=\begin{bmatrix} ...
2
votes
1answer
782 views

Relation Matrix

Is my set of related pairs correct for this problem? $$\{(2,1), (2,2), (3,1), (3,2), (3,3), (4,1), (4,2), (4,3), (4,4)\}$$ Suppose that $\,A = \{1,2,3,4\}\,$ and $\,B = \{1, 2, 3\}.$ Let ...
3
votes
2answers
162 views

transitivity of commutator

I remember a quantum mechanics lecture where my professor said "Two matrices $A, B$ which commute with a third matrix $C$, $[A,C]=[B,C]=0$, commute with each other: $[A,B]=0$." I pointed out the ...
0
votes
2answers
511 views

Relations Represented As Matrices

The question is, "How many nonzero entries does the matrix representing the relation $R$ on $A=\{1,2,3,...,100\}$ consisting of the first $100$ positive integers have if $R=\{(a, b)|a=b+1\}$? I ...
0
votes
2answers
392 views

Elementary Row Operations To Find Inverse Matrix

I have to find the inverse matrix of this matrix that represents a relation. My question is, is it possible to use elementary row operations on a one-zero matrix to find the inverse? I've done it ...
2
votes
2answers
4k views

Transitive Relation

$$\begin{bmatrix}1&0&1\\0&1&0\\1&0&1\end{bmatrix}$$ This is a matrix representation of a relation on the set $\{1, 2, 3\}$. I have to determine if this relation matrix is ...
0
votes
1answer
148 views

Relations As Matrices

I am currently reading about portraying relations on a set as matrices. Firstly, I am not sure how to determine the dimensions of the matrix when given set(s). Secondly, when I go down the columns, ...
0
votes
1answer
63 views

The productrelation matrix is equivalent to the product of the matrix of the relations

I didn't get this thing. Let $R, S$ be two relations from $A \to A$ with $A$ being an arbitrary set. And $M_R$ and $M_S$ their relation matrixes defined as: $(M_R)_{ij}=\left\{ \begin{array}{l l} ...