Matrices with all minors of some fixed order being equal: the rank, dimension and characteristic property

• Date: 2019
• Author Affiliations: D. Ya. Trebenko — Національний педагогічний університет імені М. П. Драгоманова, Київ; O. O. Trebenko
• Keywords: keywords
• Main Authors: Trebenko, D. Ya., Trebenko, O. O.
• Format: Article
• Language: Ukrainian
• Published: Інститут математики НАН України 2019
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/519
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

Investigated in this paper is aclass $\mathfrak{M}$ of matrices (over an arbitrary field) in whichall minors of some fixed order $k$ are equal and nonzero. It isestablished that the rank of such matrices equals to $k$. Thepossible values for the dimension of a matrix in $\mathfrak{M}$ arefound. A ne...