LINEAR TRANSFORMATIONS THAT PRESERVE TERM RANK BETWEEN DIFFERENT MATRIX SPACES

On certain semigroups of transformations that preserve double direction equivalence

Let TX be the full transformation semigroups on the set X. For an equivalence E on X, let TE(X) = {α ∈ TX : ∀(x, y) ∈ E ⇔ (xα, yα) ∈ E}It is known that TE(X) is a subsemigroup of TX. In this paper, we discussthe Green's *-relations, certain *-ideal and certain Rees quotient semigroup for TE(X).

Transformations that Preserve Learnability

on certain semigroups of transformations that preserve double direction equivalence

let tx be the full transformation semigroups on the set x. for an equivalence e on x, let te(x) = {α ∈ tx : ∀(x, y) ∈ e ⇔ (xα, yα) ∈ e}it is known that te(x) is a subsemigroup of tx. in this paper, we discussthe green's *-relations, certain *-ideal and certain rees quotient semigroup for te(x).

Do Linear Transformations Preserve Fuzzy Linear Independence? Some Examples

In this paper, we examine whether basic linear transformations in R 2, such as rotations, scales, etc, preserve fuzzy linear independence. We provide some examples to the contrary. Mathematics Subject Classification: 08A72, 03E72

Vector Spaces and Linear Transformations

1 Vector spaces A vector space is a nonempty set V , whose objects are called vectors, equipped with two operations, called addition and scalar multiplication: For any two vectors u, v in V and a scalar c, there are unique vectors u + v and cu in V such that the following properties are satisfied. 1. u + v = v + u, 2. (u + v) + w = u + (v + w), 3. There is a vector 0, called the zero vector, su...