Relationships between the Completion Problems for Various Classes of Matrices

نویسنده

  • Leslie Hogben
چکیده

where N = {1, . . . , n}. In this paper a pattern is assumed to include all diagonal positions. A symmetric pattern is a pattern with the property that (i, j) is in the pattern if and only if (j, i) is also in the pattern; symmetric patterns are also called positionally or combinatorially symmetric. An asymmetric pattern is a pattern with the property that if (i, j) is in the pattern, then (j, i) is not in the pattern. A partial matrix specifies the pattern if its specified entries are exactly those listed in the pattern. For a class X of real matrices, we say a pattern has Xcompletion if every partial X-matrix specifying the pattern can be completed to an X-matrix. The matrix completion problem (for patterns) for the class of Xmatrices is to determine which patterns have X-completion. Matrix completion problems have been studied for many classes of matrices, including positive definite matrices [6], P-matrices [11], [4], P0matrices [2], M-matrices [8], M0-matrices [9], inverse M-matrices [12], [7] and ______________

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

PERRON-FROBENIUS THEORY ON THE NUMERICAL RANGE FOR SOME CLASSES OF REAL MATRICES

We give further results for Perron-Frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. We indicate two techniques for establishing the main theorem ofPerron and Frobenius on the numerical range. In the rst method, we use acorresponding version of Wielandt's lemma. The second technique involves graphtheory.

متن کامل

The Effect of the Presence of Oppositional Defiant Disorder in Children on the Quality of the Relationships among their Family Members

Oppositional Defiant Disorder (ODD) is one of the most common behavioral disorders that severely damages a child’s interpersonal relationships with peers, friends, and family members. The family and the quality of its interrelationships, as the first and most enduring factor in the formation of the child’s personality and subsequent behaviors, is a determining factor in the development of menta...

متن کامل

Mutual Kernel Matrix Completion

With the huge influx of various data nowadays, extracting knowledge from them has become an interesting but tedious task among data scientists, particularly when the data come in heterogeneous form and have missing information. Many data completion techniques had been introduced, especially in the advent of kernel methods. However, among the many data completion techniques available in the lite...

متن کامل

Improving Chernoff criterion for classification by using the filled function

Linear discriminant analysis is a well-known matrix-based dimensionality reduction method. It is a supervised feature extraction method used in two-class classification problems. However, it is incapable of dealing with data in which classes have unequal covariance matrices. Taking this issue, the Chernoff distance is an appropriate criterion to measure distances between distributions. In the p...

متن کامل

Relationships between Meteorological Drought and Vegetation Degradation Using Satellite and Climatic Data in a Semi-Arid Environment in Markazi Province, Iran

The assessment of relationships between satellite-derived vegetation indices and meteorological drought improves our understanding of how these indices respond to climatic changes. The combination of climate data and the Normalized Difference Vegetation Index (NDVI) product of Moderate Resolution Imaging Spectroradiometer (MODIS) imagery provided an opportunity to evaluate the impact of d...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003