Through grounded analysis, we identified recurring concept imagery that students provided for subspace, namely, geometric object, part of whole, and algebraic object. V is called a subspace of V if W is itself a vector space under the addition and scalar multiplication defined on V. We used the analytical tools of concept image and concept definition of Tall and Vinner (Educational Studies in Mathematics, 12(2): 151-169, 1981) in order to highlight this distinction in student responses. The definition of subspace in the dictionary is a part of a mathematical matrix a subset of a space which is itself a space.

Subsection 1.6.1 Definition of a subspace. A subspace (or linear subspace) of R2 is a set of two-dimensional vectors within R2, where the set meets three specific conditions: 1) The set includes the zero vector, 2) The set is closed under scalar multiplication, and 3) The set is closed under addition. Freebase (0. subspace noun The psychological state of the submissive or 'bottom' during sadomasochistic activity. subspace noun Any (often unspecified) method of communicating faster than light. This is consistent with literature in other mathematical content domains that indicates that a learner's primary understanding of a concept is not necessarily informed by that concept's formal definition. This notion will allow us to quickly establish many more examples of vector spaces. is a vector space, using the same definition of addition and scalar multiplication as V, then U is called a subspace of V. subspace noun A subset of a space which is a space in its own right. In interviews conducted with eight undergraduates, we found students' initial descriptions of subspace often varied substantially from the language of the concept's formal definition, which is very algebraic in nature. This paper reports on a study investigating students' ways of conceptualizing key ideas in linear algebra, with the particular results presented here focusing on student interactions with the notion of subspace.

Subspace definition definition