Property of an orthogonal projection matrix

DU Kun; GU Gui-ding

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Jan. 2012

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DU Kun, GU Gui-ding. Property of an orthogonal projection matrix[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 97-99.

Citation:

DU Kun, GU Gui-ding. Property of an orthogonal projection matrix[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 97-99.

DU Kun, GU Gui-ding. Property of an orthogonal projection matrix[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 97-99.

Citation:

DU Kun, GU Gui-ding. Property of an orthogonal projection matrix[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 97-99.

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Property of an orthogonal projection matrix

DU Kun¹,
GU Gui-ding²

1.
School of finance, Shanghai University of Finance and Economics, Shanghai} 200433, China;
2.
Department of Mathematics, Shanghai University of Finance and Economics, Shanghai} 200433, China.

Received Date: 2011-04-01
Rev Recd Date: 2011-07-01
Publish Date: 2012-01-25

Abstract

Abstract

In this paper we showed that for an orthogonal projection matrix with rank $k$, there exists an principal submatrix with order $k$ of the matrix, such that its Rayleigh quotient has a positive lower bound. The proof was made by using the relation of the singular values, eigenvalues and norm of matrices, as well as the properties of unitary matrix and compound matrix.
- orthogonal projection matrix,
- singular value,
- unitary matrix,
- compound matrix

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References(1)

References

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