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Student[LinearAlgebra]

  

GramSchmidt

  

compute an orthonormal set of Vectors

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

GramSchmidt(V, options)

Parameters

V

-

list or set of Vector(s)

options

-

(optional) parameters; for a complete list, see LinearAlgebra[GramSchmidt]

Description

• 

The GramSchmidt(V) command computes a list or set of orthonormal Vectors by using the Gram-Schmidt orthogonalization process. If V is an empty list or set, GramSchmidt(V) returns an empty list or set, respectively.

• 

The number of Vectors returned is the dimension of the vector space spanned by V.  In particular, if the Vectors in V are not linearly independent, fewer Vectors than the number in V are returned.

• 

The dimension and orientation of all Vectors in V must be the same.

• 

By default in the Student[LinearAlgebra] package, complex conjugates are not used when forming dot products, including when applying the Gram-Schmidt process.  This behavior can be modified with the SetDefault command.

Examples

withStudentLinearAlgebra:

w12,1,0,1:

w21,0,2,1:

w30,2,1,0:

BGramSchmidtw1,w2,w3

B6366066,02622326,221214212121210

(1)

`.`B1,B1,`.`B1,B2,`.`B1,B3

1,0,0

(2)

GramSchmidt1|0,1|b

10,0bb2

(3)

See Also

LinearAlgebra[GramSchmidt]

Student[LinearAlgebra]

Student[LinearAlgebra][Basis]

Student[LinearAlgebra][LUDecomposition]

Student[LinearAlgebra][SetDefault]