• Title, Summary, Keyword: linear determinantal

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EXAMPLES OF SMOOTH SURFACES IN ℙ3 WHICH ARE ULRICH-WILD

  • Casnati, Gianfranco
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.2
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    • pp.667-677
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    • 2017
  • Let $F{\subseteq}{\mathbb{P}}^3$ be a smooth surface of degree $3{\leq}d{\leq}9$ whose equation can be expressed as either the determinant of a $d{\times}d$ matrix of linear forms, or the pfaffian of a $(2d){\times}(2d)$ matrix of linear forms. In this paper we show that F supports families of dimension p of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large p.

CONDENSED CRAMER RULE FOR COMPUTING A KIND OF RESTRICTED MATRIX EQUATION

  • Gu, Chao;Xu, Zhaoliang
    • Journal of applied mathematics & informatics
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    • v.26 no.5_6
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    • pp.1011-1020
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    • 2008
  • The problem of finding Cramer rule for solutions of some restricted linear equation Ax = b has been widely discussed. Recently Wang and Qiao consider the following more general problem AXB = D, $R(X){\subset}T$, $N(X){\supset}\tilde{S}$. They present the solution of above general restricted matrix equation by using generalized inverses and give an explicit expression for the elements of the solution matrix for the matrix equation. In this paper we re-consider the restricted matrix equation and give an equivalent matrix equation to it. Through the equivalent matrix equation, we derive condensed Cramer rule for above restricted matrix equation. As an application, condensed determinantal expressions for $A_{T,S}^{(2)}$ A and $AA_{T,S}^{(2)}$ are established. Based on above results, we present a method for computing the solution of a kind of restricted matrix equation.

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