More bounds for elgenvalues using traces

Wolkowicz, Henry; Styan, George P. H.

doi:10.1016/0024-3795(80)90201-3

Cited by 37 publications

(3 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The density of this sum is a convolution which is bounded by O( 1 λmax ) (after a small calculation). Moreover, by Theorem 2.1 of Wolkowicz and Styan (1980) we know that…”

Section: Appendix F Rate Of Convergencementioning

confidence: 96%

Testing for constancy in varying coefficient models

Ahkim

Verhasselt

2018

Communications in Statistics - Theory and Methods

View full text Add to dashboard Cite

We consider varying coefficient models, which are an extension of the classical linear regression models in the sense that the regression coefficients are replaced by functions in certain variables (for example time), the covariates are also allowed to depend on other variables. Varying coefficient models are popular in longitudinal data and panel data studies, and have been applied in fields such as finance and health sciences. We consider longitudinal data and estimate the coefficient functions by the flexible B-spline technique. An important question in a varying coefficient model is whether an estimated coefficient function is statistically different from a constant (or zero). We develop testing procedures based on the estimated B-spline coefficients by making use of nice properties of a B-spline basis. Our method allows longitudinal data where repeated measurements for an individual can be correlated. We obtain the asymptotic null distribution of the test statistic. The power of the proposed testing procedures are illustrated on simulated data where we highlight the importance of including the correlation structure of the response variable and on real data.

show abstract

“…The density of this sum is a convolution which is bounded by O( 1 λmax ) (after a small calculation). Moreover, by Theorem 2.1 of Wolkowicz and Styan (1980) we know that…”

Section: Appendix F Rate Of Convergencementioning

confidence: 96%

Testing for constancy in varying coefficient models

Ahkim

Verhasselt

2018

Communications in Statistics - Theory and Methods

View full text Add to dashboard Cite

show abstract

“…Theorem2 indicates that the exact eigenvalue and multiplicities of an orthogonal matrix with cube being symmetric could be obtained by Eqs. (3), which only relates to trace of matrices, avoiding to calculate the characteristic polynomials.…”

Section: Proof For the Necessity If The All Possible Eigenvalue Ofmentioning

confidence: 99%

“…A scalar λ is called an eigenvalue of an n × n complex matrix A if there is a nontrivial solution x of Ax = λx [1]. The eigenvalues of a matrix A are the roots of the det(A − λE) = 0 and so are difficult to evaluate in general [2,3]. " Computer softwares such as Mathematica and Maple can use symbolic calculations to find the characteristic polynomial of a moderatesized matrix" [4].…”

Section: Introductionmentioning

confidence: 99%

The Spectrum of the Orthogonal Matrix with its Cube being Symmetric

Chen¹,

Zhong-peng²,

Lin³

2023

Preprint

View full text Add to dashboard Cite

The orthogonal matrix with cube be symmetric is a common class of matrices with important properties. We pay attention to this kind of matrices. By using the close relationship between the eigenvalues of a matrix and the trace of its power, we obtain the algorithm for its all possible different eigenvalues and multiplicities. The calculation formula is expressed only by the trace of a matrix and its power, avoiding solving the characteristic polynomial. The method is simple and practical. Furthermore, a new essential characterization for the sum of orthogonal matrix pairs being orthogonal is given as well.

show abstract