Mathematics · Advanced university
Dimension of a quotient vector space · formula reference
W must be a linear subspace of a finite-dimensional vector space V.
Formula
W must be a linear subspace of a finite-dimensional vector space V.
dim(V/W) = dim V − dim W
Worked example
Let V be a 30-dimensional vector space and W a 17-dimensional subspace. Find dim(V/W). Round the final result to 4 decimal places if needed.
Extend a basis of W to a basis of V. The 13 added directions form a basis of the quotient.
13
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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