Weak convergence of linear rank statistics
Béla Gyires (1980)
Banach Center Publications
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Béla Gyires (1980)
Banach Center Publications
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Ramón Ardanuy, José Manuel Sánchez (1993)
Extracta Mathematicae
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In multivariate analysis it is generally assumed that the observations are normally distributed. It was Mardia ([1] to [5]), who first introduced measures of multivariate skewness and kurtosis; these statistics are affine invariant and can be used for testing multivariate normality. Skewness and kurtosis tests remain among the most powerful, general and easy to implement. In this paper we show some properties of these statistics when population distribution is singular.
Mortici, Cristinel (2003)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Chao Ma (2017)
Open Mathematics
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Let x, y be two distinct real numbers. An {x, y}-matrix is a matrix whose entries are either x or y. We determine the possible numbers of x’s in an {x, y}-matrix with a given rank. Our proof is constructive.
Tian, Yongge, Cheng, Shizhen (2003)
The New York Journal of Mathematics [electronic only]
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Cao, Chongguang, Tang, Xiaomin (2004)
International Journal of Mathematics and Mathematical Sciences
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Seok-Zun Song, Young-Bae Jun (2006)
Discussiones Mathematicae - General Algebra and Applications
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The zero-term rank of a matrix is the minimum number of lines (row or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve the zero-term rank of the m × n integer matrices. That is, a linear operator T preserves the zero-term rank if and only if it has the form T(A)=P(A ∘ B)Q, where P, Q are permutation matrices and A ∘ B is the Schur product with B whose entries are all nonzero integers.
Yong Ge Tian, George P. H. Styan (2002)
Commentationes Mathematicae Universitatis Carolinae
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It is shown that where is idempotent, has full row rank and . Some applications of the rank formula to generalized inverses of matrices are also presented.
Duanmei Zhou, Guoliang Chen, Jiu Ding (2017)
Open Mathematics
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Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX. Together with a previous paper devoted to the case that QTP is nonsingular, we have completely solved the matrix equation with any given matrix A of rank-two.
Beasley, LeRoy B. (1999)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Hans Havlicek, Peter Šemrl (2006)
Studia Mathematica
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We characterize bijections on matrix spaces (operator algebras) preserving full rank (invertibility) of differences of matrix (operator) pairs in both directions.