latent roots
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Bounds for the zeros of unilateral octonionic polynomials

Analele Universitatii Ovidius Constanta - Seria Matematica ◽

10.2478/auom-2021-0043 ◽

2021 ◽

Vol 29 (3) ◽

pp. 243-267

Author(s):

Rogério Serôdio ◽

P. D. Beites ◽

José Vitória

Keyword(s):

Lower Bounds ◽

Conjugacy Classes ◽

Upper And Lower Bounds ◽

Matrix Polynomials ◽

Matrix Norms ◽

Abstract In the present work it is proved that the zeros of a unilateral octonionic polynomial belong to the conjugacy classes of the latent roots of an appropriate lambda-matrix. This allows the use of matricial norms, and matrix norms in particular, to obtain upper and lower bounds for the zeros of unilateral octonionic polynomials. Some results valid for complex and/or matrix polynomials are extended to octonionic polynomials.

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Polynomial traces and elementary symmetric functions in the latent roots of a non-central Wishart matrix

Journal of Multivariate Analysis ◽

10.1016/j.jmva.2020.104629 ◽

2020 ◽

Vol 179 ◽

pp. 104629

Author(s):

Elvira Di Nardo

Keyword(s):

Symmetric Functions ◽

Wishart Matrix ◽

Elementary Symmetric Functions ◽

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Matrix-variate distribution theory under elliptical models-4: Joint distribution of latent roots of covariance matrix and the largest and smallest latent roots

Journal of Multivariate Analysis ◽

10.1016/j.jmva.2015.12.012 ◽

2016 ◽

Vol 145 ◽

pp. 224-235 ◽

Author(s):

Francisco J. Caro-Lopera ◽

Graciela González Farías ◽

Narayanaswamy Balakrishnan

Keyword(s):

Covariance Matrix ◽

Joint Distribution ◽

Distribution Theory ◽

Elliptical Models ◽

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ASYMPTOTIC DISTRIBUTIONS OF LIKELIHOOD RATIO CRITERIA FOR TESTING LATENT ROOTS AND LATENT VECTORS OF A COVARIANCE MATRIX UNDER AN ELLIPTICAL POPULATION

Volume 1, Nonparametric Methods in Statistics and Related Topics ◽

10.1515/9783110917819.651 ◽

2013 ◽

Author(s):

TAKESI HAYAKAWA ◽

MADAN L. PURI

Keyword(s):

Covariance Matrix ◽

Likelihood Ratio ◽

Asymptotic Distributions ◽

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Transfer Function and Network Synthesis of Electrical Fast Transient/Burst Generator Based on Latent-Roots Method

IEEE Transactions on Electromagnetic Compatibility ◽

10.1109/temc.2010.2053934 ◽

2010 ◽

Vol 52 (4) ◽

pp. 790-796

Author(s):

Xiaoshe Zhai ◽

Jianhua Wang ◽

Yingsan Geng ◽

Li Yu ◽

Zhiyuan Liu

Keyword(s):

Transfer Function ◽

Network Synthesis ◽

Fast Transient ◽

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Prediction and assignment of latent roots of damped asymmetric systems by structural modifications

Mechanical Systems and Signal Processing ◽

10.1016/j.ymssp.2008.08.001 ◽

2009 ◽

Vol 23 (6) ◽

pp. 1920-1930 ◽

Author(s):

Huajiang Ouyang

Keyword(s):

Structural Modifications ◽

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A receptance-based method for predicting latent roots and critical points in friction-induced vibration problems of asymmetric systems

Journal of Sound and Vibration ◽

10.1016/j.jsv.2008.10.020 ◽

2009 ◽

Vol 321 (3-5) ◽

pp. 1058-1068 ◽

Author(s):

Huajiang Ouyang ◽

Luis Baeza ◽

Shaolin Hu

Keyword(s):

Critical Points ◽

Vibration Problems ◽

Friction Induced Vibration ◽

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NUMERICAL COMPUTATION ON DISTRIBUTIONS OF THE LARGEST AND THE SMALLEST LATENT ROOTS OF THE WISHART MATRIX

Journal of the Japanese Society of Computational Statistics ◽

10.5183/jjscs1988.19.45 ◽

2006 ◽

Vol 19 (1) ◽

pp. 45-56 ◽

Author(s):

Hiroki Hashiguchi ◽

Naoto Niki

Keyword(s):

Numerical Computation ◽

Wishart Matrix ◽

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NONPARAMETRIC TEST FOR EQUALITY OF INTERMEDIATE LATENT ROOTS IN NON-NORMAL DISTRIBUTION

Journal of the Japanese Society of Computational Statistics ◽

10.5183/jjscs1988.11.9 ◽

1998 ◽

Vol 11 (1) ◽

pp. 9-23

Author(s):

Kenji Ushizawa ◽

Yoshiharu Sato ◽

Takakazu Sugiyama

Keyword(s):

Normal Distribution ◽

Nonparametric Test ◽

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A NON-PARAMETRIC METHOD TO TEST EQUALITY OF INTERMEDIATE LATENT ROOTS OF TWO POPULATIONS IN A PRINCIPAL COMPONENT ANALYSIS

JOURNAL OF THE JAPAN STATISTICAL SOCIETY ◽

10.14490/jjss1995.28.227 ◽

1998 ◽

Vol 28 (2) ◽

pp. 227-235 ◽

Author(s):

Takakazu Sugiyama ◽

Kenji Ushizawa

Keyword(s):

Principal Component Analysis ◽

Parametric Method ◽

Principal Component ◽

Component Analysis ◽

Two Populations ◽

Latent Roots ◽

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