2
votes
1answer
35 views

Boolean Least Squares semidefinite relaxation

So I'm working on the Boolean least squares problem that comes up a lot in circuit design. In its raw form, it looks like this, $$\phi = \min \operatorname{trace}(A^TAX) - 2b^TAx + b^Tb$$ s.t. $$X = ...
0
votes
1answer
37 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 ...
2
votes
0answers
75 views

Matrix of integers to boolean matrix

My Question is about converting a matrix of numbers, say each row is an item and each column is a feature of the item. The features are currently integers but I want to convert the feature ...
10
votes
2answers
320 views

A matrix w/integer eigenvalues and trigonometric identity

Any intuition and/or rigorous arguments on the proofs of the following statements would be appreciated: Let $n$ be a natural number. (a) Consider the following Toeplitz/circulant symmetric matrix: ...
0
votes
0answers
135 views

Given a state transformation matrix and a state vector, how to find the total number of changes for each individual element.

I have a vector of binary variables, $s$ representing a state at some point in time, and a transformation matrix $T$. The initial state is $s_0$. $s_n = Ts_{n-1}$ Given a number of transformations, ...
6
votes
2answers
317 views

Is there an $O(n^2)$ test to determine if an $n \times n$ Boolean matrix $B$ has an inverse?

D.E. Rutherford shows that if a Boolean matrix $B$ has an inverse, then $B^{-1}= B^T$, or $BB^T=B^TB=I$. I have two related questions: The only invertible Boolean matrices I can find are ...