Applications of the matrix operators vech and vec

Jinadasa, K.G.

doi:10.1016/0024-3795(88)90143-7

Cited by 6 publications

(3 citation statements)

References 7 publications

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“…By analogy with the finite dimensional case [30], it is customary to write κ = vec(T κ ), where the vec(•) operator maps an infinitedimensional linear operator onto its associated kernel representation.…”

Section: Population Versionmentioning

confidence: 99%

SIML: Sieved Maximum Likelihood for Array Signal Processing

Simeoni

Hurley

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Stochastic Maximum Likelihood (SML) is a popular direction of arrival (DOA) estimation technique in array signal processing. It is a parametric method that jointly estimates signal and instrument noise by maximum likelihood, achieving excellent statistical performance. Some drawbacks are the computational overhead as well as the limitation to a point-source data model with fewer sources than sensors. In this work, we propose a Sieved Maximum Likelihood (SiML) method. It uses a general functional data model, allowing an unrestricted number of arbitrarily-shaped sources to be recovered. To this end, we leverage functional analysis tools and express the data in terms of an infinite-dimensional sampling operator acting on a Gaussian random function. We show that SiML is computationally more efficient than traditional SML, resilient to noise, and results in much better accuracy than spectral-based methods.

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Section: Population Versionmentioning

confidence: 99%

SIML: Sieved Maximum Likelihood for Array Signal Processing

Simeoni

Hurley

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…The study of the application 𝑣𝑒𝑐 and 𝑣𝑒𝑐ℎ was carried out by [1], with a focused study on the symmetric matrix in developing multivariate statistical results. Furthermore, other applications of 𝑣𝑒𝑐 and 𝑣𝑒𝑐ℎ were carried out by [2], referred to [1], to obtain a generalization of some of the matrix results given by [3]. In particular, the variance-covariance matrix of the Wishart distribution is obtained in a very compact nonsingular form.…”

Section: Introductionmentioning

confidence: 99%

On The Relationship Between The Matrix Operators of vech* and vecp*

Hidayah,

Yanita,

Nazra

2023

IJPSAT

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“…The 𝑣𝑒𝑐 operator then inspires the creation of new operators with similar transformations, making the matrix a column vector. Operators who were later born were 𝑣𝑒𝑐ℎ, 𝑣𝑒𝑐𝑑, 𝑣𝑒𝑐𝑝, and 𝑣𝑒𝑐𝑏 operators (see [3], [4], [5], [6], and [7]). With the new operators after the 𝑣𝑒𝑐 operator, the relation between each operator is also created.…”

Section: Introductionmentioning

confidence: 99%

On the Commutation Matrix

Yanita,

Yulianti

2023

BAREKENG: J. Math. & App.

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The commutation matrix is a matrix that transforms any vec matrix , to vec transpose . In this article, three definitions of the commutation matrix are presented in different ways. It is shown that these three definitions are equivalent. Proof of the equivalent uses the properties in the Kronecker product on the matrix. We also gave the example of the commutation matrix using three ways as Moreover, in this study, we investigate the properties of the commutation matrix related to its transpose and the relation between the vec matrix and the vec transpose matrix using the commutation matrix. We have that the transpose and the inverse of the commutation matrix is its transpose.

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Applications of the matrix operators vech and vec

Cited by 6 publications

References 7 publications

SIML: Sieved Maximum Likelihood for Array Signal Processing

SIML: Sieved Maximum Likelihood for Array Signal Processing

On The Relationship Between The Matrix Operators of vech* and vecp*

On the Commutation Matrix

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