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On Factorization of M-Channel Paraunitary Filterbanks - Gao, Nguyen, Strang (2001) (1 citation) (Correct)
....orthogonal and angles , the matrix produced by (64) is an orthogonal matrix of the form , where and are symmetric. In the following, we prove the converse. The orthogonality of implies that . Since and are symmetric, For these commuting matrices, there exists an orthogonal matrix so that [31] (65) where and are diagonal matrices containing the eigenvalues of and . The above equation means that we can express as in (64) The orthogonality of also implies that . Substituting (65) into it, we have . Therefore, we can express and by angles as stated in the lemma. This completes the ....
J. R. Schott, Matrix Analysis for Statistics. New York: Wiley, 1997.
On Factorization of M-Channel Paraunitary Filterbanks - Gao, Nguyen, Strang (2001) (1 citation) (Correct)
....A = A 0 A 1 A 1 A 0 , where A 0 and A 1 are symmetric. In the following, we prove the converse. The orthogonality of A implies that A T 1 A 0 = A T 0 A 1 . Since A 0 and A 1 are symmetric, A 1 A 0 = A 0 A 1 . For these commuting matrices, there exists an orthogonal matrix V so that [30] A 0 = VCV T ; A 1 = VSV T (65) where C and S are diagonal matrices containing the eigenvalues of A 0 and A 1 . The above equation means that we can express A as in (64) The orthogonality of A also implies that A T 0 A 0 A T 1 A 1 = 22 I. Substituting (65) into it, we have C 2 S ....
J. R. Schott, Matrix Analysis for Statistics, Wiley-Interscience, New York, 1997.
Pace Regression - Wang, Witten (1999) (Correct)
.... classic ols estimate c M, which has parameter vector b = X 0 X) 1 X 0 y, provides a basis for such a relationship, because it is well known that for all j, A j ( c M) are independently, noncentrally 2 distributed with one degree of freedom and noncentrality parameter A j (M ) 2 (Schott, 1997, p390) We write this as A j ( c M) 2 1 (A j (M ) 2) independently for all j: 13) When 2 is unknown and therefore replaced by the unbiased ols estimate 2 , the 2 distribution in (13) becomes an F distribution: A j ( c M) F (1; n k; A j (M ) 2) independently for ....
Schott, J. R. (1997). Matrix analysis for statistics. New York: Wiley.
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Schott, J. R. Matrix Analysis for Statistics. Wiley, 1997.
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J. R. Schott. Matrix analysis for statistics. New York: John Wiley & Sons, 1997.
Maximum likelihood spatiotemporal EEG/MEG source analysis - Huizenga, Waldorp, Grasman (Correct)
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J.R. Schott, Matrix analysis for statistics. New York: Wiley, 1997.
Flux Estimation Using Incomplete Isotopomer Information - Rousu, Rantanen, Ukkonen (2002) (Correct)
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Schott, J. Matrix analysis for statistics. Wiley, 1997
Numerically Stable Generation of Correlation Matrices and.. - Davies, Higham (1999) (5 citations) (Correct)
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James R. Schott. Matrix Analysis for Statistics. Wiley, New York, 1997. xii+426 pp. ISBN 0-471-15409-1.
Generating Test Matrices for the One- and Two-Sided Jacobi.. - Davies, Higham (1999) (Correct)
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James R. Schott. Matrix Analysis for Statistics. Wiley, New York, 1997. xii+426 pp. ISBN 0-471-15409-1.
Space-Time Block-Coded OFDMA With Linear Precoding for.. - Stamoulis, Liu.. (2002) (1 citation) (Correct)
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J. R. Schott, Matrix Analysis for Statistics. New York: Wiley, 1997.
Numerically Stable Generation of Correlation Matrices and.. - Davies, Higham (2000) (5 citations) (Correct)
No context found.
James R. Schott. Matrix Analysis for Statistics. Wiley, New York, 1997. xii+426 pp. ISBN 0-471-15409-1.
Numerically Stable Generation of Correlation Matrices and.. - Davies, Higham (1999) (5 citations) (Correct)
No context found.
James R. Schott. Matrix Analysis for Statistics. Wiley, New York, 1997. xii+426 pp. ISBN 0-471-15409-1.
Generating Test Matrices for the One- and Two-Sided Jacobi.. - Davies, Higham (1999) (Correct)
No context found.
James R. Schott. Matrix Analysis for Statistics. Wiley, New York, 1997. xii+426 pp. ISBN 0-471-15409-1.
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