Appendix:Glossary of linear algebra
Definition from Wiktionary, the free dictionary
This is a glossary of linear algebra.
- affine transformation
- A linear transformation between vector spaces followed by a translation.
- In a vector space, a linearly independent set of vectors spanning the whole vector space.
- The unique scalar function over square matrices which is distributive over matrix multiplication, multilinear in the rows and columns, and takes the value of 1 for the unit matrix.
- diagonal matrix
- A matrix in which only the entries on the main diagonal are non-zero.
- The number of elements of any basis of a vector space.
- identity matrix
- A diagonal matrix all of the diagonal elements of which are equal to 1.
- inverse matrix
- Of a matrix A, another matrix B such that A multiplied by B and B multiplied by A both equal the identity matrix.
- linear algebra
- The branch of mathematics that deals with vectors, vector spaces, linear transformations and systems of linear equations.
- linear combination
- A sum, each of whose summands is an appropriate vector times an appropriate scalar (or ring element).
- linear equation
- A polynomial equation of the first degree (such as x = 2y - 7).
- linear transformation
- A map between vector spaces which respects addition and multiplication.
- linearly independent
- (Of a set of vectors or ring elements) whose nontrivial linear combinations are nonzero.
- A rectangular arrangement of numbers or terms having various uses such as transforming coordinates in geometry, solving systems of linear equations in linear algebra and representing graphs in graph theory.
- Of a bounded linear operator A, the scalar values λ such that the operator A—λI, where I denotes the identity operator, does not have a bounded inverse.
- square matrix
- A matrix having the same number of rows as columns.
- A directed quantity, one with both magnitude and direction; an element of a vector space.
- vector space
- A set V, whose elements are called "vectors", together with a binary operation + forming a module (V,+), and a set F* of bilinear unary functions f*:V→V, each of which corresponds to a "scalar" element f of a field F, such that the composition of elements of F* corresponds isomorphically to multiplication of elements of F, and such that for any vector v, 1*(v) = v.