Next: Functions and Variables for linearalgebra, Up: linearalgebra [Contents][Index]
linearalgebra
is a collection of functions for linear algebra.
Example:
(%i1) M : matrix ([1, 2], [1, 2]); [ 1 2 ] (%o1) [ ] [ 1 2 ] (%i2) nullspace (M); [ 1 ] [ ] (%o2) span([ 1 ]) [ - - ] [ 2 ] (%i3) columnspace (M); [ 1 ] (%o3) span([ ]) [ 1 ] (%i4) ptriangularize (M - z*ident(2), z); [ 1 2 - z ] (%o4) [ ] [ 2 ] [ 0 3 z - z ] (%i5) M : matrix ([1, 2, 3], [4, 5, 6], [7, 8, 9]) - z*ident(3); [ 1 - z 2 3 ] [ ] (%o5) [ 4 5 - z 6 ] [ ] [ 7 8 9 - z ] (%i6) MM : ptriangularize (M, z); [ 4 5 - z 6 ] [ ] [ 2 ] [ 66 z 102 z 132 ] [ 0 -- - -- + ----- + --- ] (%o6) [ 49 7 49 49 ] [ ] [ 3 2 ] [ 49 z 245 z 147 z ] [ 0 0 ----- - ------ - ----- ] [ 264 88 44 ] (%i7) algebraic : true; (%o7) true (%i8) tellrat (MM [3, 3]); 3 2 (%o8) [z - 15 z - 18 z] (%i9) MM : ratsimp (MM); [ 4 5 - z 6 ] [ ] [ 2 ] (%o9) [ 66 7 z - 102 z - 132 ] [ 0 -- - ------------------ ] [ 49 49 ] [ ] [ 0 0 0 ] (%i10) nullspace (MM); [ 1 ] [ ] [ 2 ] [ z - 14 z - 16 ] [ -------------- ] (%o10) span([ 8 ]) [ ] [ 2 ] [ z - 18 z - 12 ] [ - -------------- ] [ 12 ] (%i11) M : matrix ([1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]); [ 1 2 3 4 ] [ ] [ 5 6 7 8 ] (%o11) [ ] [ 9 10 11 12 ] [ ] [ 13 14 15 16 ] (%i12) columnspace (M); [ 1 ] [ 2 ] [ ] [ ] [ 5 ] [ 6 ] (%o12) span([ ], [ ]) [ 9 ] [ 10 ] [ ] [ ] [ 13 ] [ 14 ] (%i13) apply ('orthogonal_complement, args (nullspace (transpose (M)))); [ 0 ] [ 1 ] [ ] [ ] [ 1 ] [ 0 ] (%o13) span([ ], [ ]) [ 2 ] [ - 1 ] [ ] [ ] [ 3 ] [ - 2 ]
Next: Functions and Variables for linearalgebra, Up: linearalgebra [Contents][Index]