Projection Matrix

Author

Eric W. Weisstein
Spectember 3, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/LinearAlgebra/ProjectionMatrix.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/ProjectionMatrix.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

Code by Todd Rowland
May 5, 2000

Initialization

<<LinearAlgebra`Orthogonalization`;

Code

ProjectionMatrixQ[a_List?MatrixQ]:=(a.a==a)

Gives the Hermitian projection matrix onto a complex subspace, given a basis.

HermitianProjectMatrixOntoBasis[a_List?MatrixQ]:=Module[{a1=GramSchmidt[a,InnerProduct->(#1.Conjugate[#2]&)]},Transpose[a1].a1
]

Examples

ProjectionMatrixQ[{{0,1},{0,1}}]