NullSpace

NullSpace(matrix)

returns a list of vectors that span the nullspace of the matrix.

See:

• Wikipedia - Kernel (linear algebra)
• Youtube - Inverse matrices, column space and null space | Essence of linear algebra, chapter 7

Examples

>> NullSpace({{1,0,-3,0,2,-8},{0,1,5,0,-1,4},{0,0,0,1,7,-9},{0,0,0,0,0,0}})
{{3,-5,1,0,0,0},
 {-2,1,0,-7,1,0},
 {8,-4,0,9,0,1}}

>> NullSpace({{1, 2, 3}, {4, 5, 6}, {7, 8, 9}})
{{1,-2,1}}

>> A = {{1, 1, 0}, {1, 0, 1}, {0, 1, 1}}
>> NullSpace(A)
{}

>> MatrixRank(A)
3

Argument {1, {2}} at position 1 is not a non-empty rectangular matrix.

>> NullSpace({1, {2}})
NullSpace({1, {2}})

Implementation status

• ✅ - full supported

Github

• Implementation of NullSpace