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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.

dim(V) = |basis|

Dimension = number of basis vectors

dim(ℝⁿ) = n

Dimension of ℝⁿ

예제 1★★☆☆☆

Find the standard basis of ℝ².

예제 2★★★☆☆

Check if (1, 2) and (2, 4) form a basis for ℝ².

Feature space dimensions

Degrees of freedom

#linear-algebra#basis#dimension#advanced