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linalg[rowspace] - compute a basis for the row space
linalg[colspace] - compute a basis for the column space
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Calling Sequence
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rowspace(A)
colspace(A)
rowspace(A, 'dim')
colspace(A, 'dim')
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Parameters
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A
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matrix
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'dim'
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(optional) unevaluated name
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Description
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The functions rowspace(A) and colspace(A) return a set of vectors that form a basis for the vector space spanned by the rows and columns of the matrix A, respectively. The vectors are returned in a canonical form with leading entries 1.
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The optional second parameter 'dim' is assigned the rank of A, which is the dimension of the row and column space.
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These functions are part of the linalg package, and so can be used in the form rowspace(..) only after performing the command with(linalg) or with(linalg, rowspace). They can always be accessed in the long form linalg[rowspace](..).
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Examples
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Important: The linalg package has been deprecated. Use the superseding packages, LinearAlgebra and VectorCalculus, instead.
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![A := matrix(3, 2, [2, 0, 3, 4, 0, 5])](/support/helpjp/helpview.aspx?si=6183/file07355/math135.png)
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![A := matrix([[2, 0], [3, 4], [0, 5]])](/support/helpjp/helpview.aspx?si=6183/file07355/math138.png)
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![{vector([0, 1]), vector([1, 0])}](/support/helpjp/helpview.aspx?si=6183/file07355/math145.png)
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![{vector([0, 1, 5/4]), vector([1, 0, -15/8])}](/support/helpjp/helpview.aspx?si=6183/file07355/math152.png)
| (3) |
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![B := array([[0, 0, 0, 1, 0], [0, x, 0, 0, 0], [0, 0, y, y, 0], [0, x, 0, 1, 0]])](/support/helpjp/helpview.aspx?si=6183/file07355/math156.png)
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![B := matrix([[0, 0, 0, 1, 0], [0, x, 0, 0, 0], [0, 0, y, y, 0], [0, x, 0, 1, 0]])](/support/helpjp/helpview.aspx?si=6183/file07355/math159.png)
| (4) |
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![{vector([0, 0, 0, 1, 0]), vector([0, 0, 1, 0, 0]), vector([0, 1, 0, 0, 0])}](/support/helpjp/helpview.aspx?si=6183/file07355/math166.png)
| (5) |
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![C := matrix(3, 3, [15/4, -3*sqrt(10)*(1/4), (1/4)*sqrt(165), -3*sqrt(10)*(1/4), 3/2, -(1/4)*sqrt(66), (1/4)*sqrt(165), -(1/4)*sqrt(66), 11/4])](/support/helpjp/helpview.aspx?si=6183/file07355/math170.png)
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![C := matrix([[15/4, -(3/4)*10^(1/2), (1/4)*165^(1/2)], [-(3/4)*10^(1/2), 3/2, -(1/4)*66^(1/2)], [(1/4)*165^(1/2), -(1/4)*66^(1/2), 11/4]])](/support/helpjp/helpview.aspx?si=6183/file07355/math173.png)
| (6) |
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Warning, unable to find a provably non-zero pivot
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![{vector([0, 0, 1]), vector([0, 1, 0]), vector([1, 0, 0])}](/support/helpjp/helpview.aspx?si=6183/file07355/math183.png)
| (7) |
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