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Basis And Dimension Calculator

Work out basis and dimension instantly with clear inputs, formula shown and shareable results.

About Basis And Dimension Calculator

A basis is a smallest spanning set. Placing the vectors as columns and row reducing finds which are independent; the pivot positions pick out a basis and their count is the dimension.

Formula

Dimension

dim(span) = rank of the matrix whose columns are the vectors

Worked example

With the default values below, Basis And Dimension Calculator returns Dimension of the span of 2. Change any input above and every figure here is recalculated in your browser.

Inputs used

Vectors listed one after another
1, 2, 3, 2, 4, 6, 1, 0, 1
Entries per vectoraccepts 1–8
3

Results

Dimension of the span
2
A basis for the span
(1, 2, 3) (1, 0, 1)
Vectors given
3
Redundant vectors
1

Step by step

  1. 1Values used
  2. 2Dimension
  3. 3Dimension of the span= 2
  4. 4A basis for the span= (1, 2, 3) (1, 0, 1)
  5. 5Vectors given= 3
  6. 6Redundant vectors= 1

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For (1,2,3), (2,4,6) and (1,0,1)?

The second is twice the first, so the span has dimension 2 with one redundant vector.

Can a space have several bases?

Yes, infinitely many, but every basis of a given space has exactly the same number of vectors.

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