A note on the representability of binary quadratic forms with Gaussian integer coefficients as sums of squares of two linear forms
John Hardy (1968)
Acta Arithmetica
Similarity:
Displaying similar documents to “A note on the representability of quaternary quadratic forms as sums of squares of two linear forms”
A note on the representability of binary quadratic forms with Gaussian integer coefficients as sums of squares of two linear forms
A Positive Definite Binary Quadratic Form as a Sum of Five Squares of Linear Forms (Completion of Mordell's Proof)
A. Schinzel (2013)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
The paper completes an incomplete proof given by L. J. Mordell in 1930 of the following theorem: every positive definite classical binary quadratic form is the sum of five squares of linear forms with integral coefficients.
Note to the Paper "A Positive Definite Binary Quadratic Form as a Sum of Five Squares of Linear Forms (Completion of Mordell's Proof)" (Bull. Polish Acad. Sci. Math. 61 (2013), 23-26)
A. Schinzel (2013)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
Representations of squares by certain quinary quadratic forms
Shaun Cooper, Heung Yeung Lam, Dongxi Ye (2013)
Acta Arithmetica
Similarity:
Sums of Squares Coprime in Pairs
Jörg Brüdern (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
Asymptotic formulae are provided for the number of representations of a natural number as the sum of four and of three squares that are pairwise coprime.
Sums of Squares of Linear Forms.
R. Baeza, D. Leep, M. O'Ryan (1986)
Mathematische Zeitschrift
Similarity:
On the representation of a binary quadratic form as a sum of squares of linear forms
L. J., Mordell (1932)
Mathematische Zeitschrift
Similarity:
Quadratic Functions of Forms. Sums of whose Values give all positive Integers
L. E. Dickson (1928)
Journal de Mathématiques Pures et Appliquées
Similarity:
Bounds for quadratic Waring's problem
Myung-Hwan Kim, Byeong-Kweon Oh (2002)
Acta Arithmetica
Similarity:
Least Squares with a Quadratic Constraint.
W. Gander (1980/81)
Numerische Mathematik
Similarity:
Characterizing experimental designs by properties of the standard quadratic forms of observations
Czesław Stępniak (2007)
Applicationes Mathematicae
Similarity:
For any orthogonal multi-way classification, the sums of squares appearing in the analysis of variance may be expressed by the standard quadratic forms involving only squares of the marginal and total sums of observations. In this case the forms are independent and nonnegative definite. We characterize all two-way classifications preserving these properties for some and for all of the standard quadratic forms.
Matrix rank/inertia formulas for least-squares solutions with statistical applications
Yongge Tian, Bo Jiang (2016)
Special Matrices
Similarity:
Least-Squares Solution (LSS) of a linear matrix equation and Ordinary Least-Squares Estimator (OLSE) of unknown parameters in a general linear model are two standard algebraical methods in computational mathematics and regression analysis. Assume that a symmetric quadratic matrix-valued function Φ(Z) = Q − ZPZ0 is given, where Z is taken as the LSS of the linear matrix equation AZ = B. In this paper, we establish a group of formulas for calculating maximum and minimum ranks and inertias...