TeXipedia

dim

Represents the dimension of a vector space or algebraic structure in mathematics.

Overview

Essential in linear algebra and abstract mathematics for denoting the number of independent vectors in a basis or the dimension of mathematical objects.

  • Commonly used in theoretical mathematics and physics to specify vector space dimensions
  • Appears frequently in linear transformations and basis calculations
  • Important in describing properties of mathematical structures like rings, fields, and modules
  • Often encountered in academic papers and advanced mathematical texts discussing algebraic structures

Examples

Showing the dimension of a vector space V.

dim⁡V=n\dim V = n 
\dim V = n

Expressing the dimension of the kernel in linear algebra.

dim⁡ker⁡(T)+dim⁡im(T)=dim⁡V\dim \ker(T) + \dim \text{im}(T) = \dim V 
\dim \ker(T) + \dim \text{im}(T) = \dim V

Calculating dimension in a direct sum of vector spaces.

dim⁡(U⊕W)=dim⁡U+dim⁡W\dim(U \oplus W) = \dim U + \dim W 
\dim(U \oplus W) = \dim U + \dim W