# Revision history [back]

Both f and lf are maps, not matrices. The option side only apply on linear_transformation when it is built from a matrix (there in an ambiguity since a matrix creates two linear maps depending on whether one consider the action on the left or on the right). In Sage, the matrix are by default acting on the right (i mean vectors are on the left), which is what you see in the representation of lf. There is no problem here:

sage: f([0,1])
(3, -1)
sage: lf([0,1])
(3.00000000000000, -1.00000000000000)
sage: f([1,0])
(2, 5)
sage: lf([1,0])
(2.00000000000000, 5.00000000000000)


Now if you want the matrix associated to the linear map lf with respect to the canonical basis, you can ask:

sage: lf.matrix(side='right')
[ 2.00000000000000  3.00000000000000]
[ 5.00000000000000 -1.00000000000000]


or

sage: lf.matrix(side='left')
[ 2.00000000000000  5.00000000000000]
[ 3.00000000000000 -1.00000000000000]


depending on whether you want the action to be on the left or on the right.

Both f and lf are maps, not matrices. The option side only apply on linear_transformation when it is built from a matrix (there in an ambiguity since a matrix creates two linear maps depending on whether one consider the action on the left or on the right). In Sage, the matrix are by default acting on the right (i mean vectors are on the left), left, see for example the .kernel() method), which is what you see in the representation of lf. There is no problem here:

sage: f([0,1])
(3, -1)
sage: lf([0,1])
(3.00000000000000, -1.00000000000000)
sage: f([1,0])
(2, 5)
sage: lf([1,0])
(2.00000000000000, 5.00000000000000)


Now if you want the matrix associated to the linear map lf with respect to the canonical basis, you can ask:

sage: lf.matrix(side='right')
[ 2.00000000000000  3.00000000000000]
[ 5.00000000000000 -1.00000000000000]


or

sage: lf.matrix(side='left')
[ 2.00000000000000  5.00000000000000]
[ 3.00000000000000 -1.00000000000000]


depending on whether you want the action to be on the left or on the right.

Both f and lf are maps, not matrices. Ther is no ambiguity on the side of the action. The side option side only apply on linear_transformationapplies on linear_transformation() when it is built from a matrix (there in an ambiguity since a matrix creates two linear maps depending on whether one consider the action on the left or on the right). In Sage, the matrix are by default acting on the right (i mean vectors are on the left, see for example the .kernel() method), which is what you see in the representation representation of lf. There is no problem here:

 sage: f([0,1]) (3, -1) sage: lf([0,1]) (3.00000000000000, -1.00000000000000) sage: f([1,0]) (2, 5) sage: lf([1,0]) (2.00000000000000, 5.00000000000000) Now Now, if you want the matrix associated to the linear map lf with respect to the canonical basis, you can ask: sage: lf.matrix(side='right') [ 2.00000000000000 3.00000000000000] [ 5.00000000000000 -1.00000000000000] or sage: lf.matrix(side='left') [ 2.00000000000000 5.00000000000000] [ 3.00000000000000 -1.00000000000000] depending on whether you want the action matrix to be act on the left or on the right. 

 4 No.4 Revision updated 2014-05-05 23:25:39 -0600 Both f and lf are maps, not matrices. Ther is no ambiguity on the side of the action. The side option only applies on linear_transformation() when it is built from a matrix (there in is an ambiguity since a matrix creates two linear maps depending on whether one consider the action on the left or on the right). In Sage, the matrix are by default acting on the right (i mean vectors are on the left, see for example the .kernel() method), which is what you see in the representation of lf. There is no problem here: sage: f([0,1]) (3, -1) sage: lf([0,1]) (3.00000000000000, -1.00000000000000) sage: f([1,0]) (2, 5) sage: lf([1,0]) (2.00000000000000, 5.00000000000000) Now, if you want the matrix associated to the linear map lf with respect to the canonical basis, you can ask: sage: lf.matrix(side='right') [ 2.00000000000000 3.00000000000000] [ 5.00000000000000 -1.00000000000000] or sage: lf.matrix(side='left') [ 2.00000000000000 5.00000000000000] [ 3.00000000000000 -1.00000000000000] depending on whether you want the matrix to act on the left or on the right. 


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