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Student[LinearAlgebra]

  

ProjectionMatrix

  

construct the matrix of the orthogonal projection onto a subspace

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

ProjectionMatrix(S, options)

Parameters

S

-

{set, list}(Vector); Vectors spanning the subspace to project onto

options

-

(optional); constructor options for the result object

Description

• 

The ProjectionMatrix(S) command constructs the matrix of the orthogonal linear projection onto the subspace spanned by the vectors in S.  If B is a maximal, linearly independent subset of S and M is the Matrix whose columns are the Vectors in B, then

ProjectionMatrixS=M·MTypesetting:-_Hold%T·M-1·MTypesetting:-_Hold%T

• 

Additional arguments are passed as options to the Matrix constructor which builds the result.

Examples

withStudentLinearAlgebra:

S1,2,3,4,4,3,2,1

S1234,4321

(1)

PProjectionMatrixS

P7102511015253101511011015310251511025710

(2)

v1,0,1,3

v10−13

(3)

w`.`P,v

w012132

(4)

BasisopS,w=S

1234,4321=1234,4321

(5)

`.`w,vw

0

(6)

ProjectionMatrixa,1

a2a2+1aa2+1aa2+11a2+1

(7)

Compatibility

• 

The Student[LinearAlgebra][ProjectionMatrix] command was introduced in Maple 17.

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

Matrix

Student[LinearAlgebra]

Vector