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Basis and Dimension
Undergraduate
Definition
A basis is a set of linearly independent vectors that span the space. Dimension is the number of basis vectors.
Formulas
dim(V) = |basis|
Dimension = number of basis vectors
dim(ℝⁿ) = n
Dimension of ℝⁿ
Examples
Example 1
Find the standard basis of ℝ².
Example 2
Check if (1, 2) and (2, 4) form a basis for ℝ².
Applications
Data Science
Feature space dimensions
Physics
Degrees of freedom
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