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- 件名homogeneous cones symmetric cones basic relative invariants
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- 件名homogeneous cones relative invariants symmetric cones principal minors oriented graphs
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- 要約等<p>In this paper, we characterize irreducible symmetric cones among homogeneous cones Ω<i> </i>of rank <i>r </i>by the fact that the basic relative invariants for Ω<i> </i>and for Ω<sup>∗ </sup>(the dual cone of Ω) both have the degrees 1<i>, </i>2<i>......>, up to permutations.</p>
- 件名homogeneous cones relative invariants symmetric cones principal minors oriented graphs
- 参照A SHORTER PROOF OF A CHARACTERIZATION OF SYMMETRIC CONES BY THE DEGREES OF THE BASIC RELATIVE INVARIANTS
デジタル記事
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デジタル記事
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- 要約等<p>The aim of this paper is to give a shorter proof to the main theorem of Yamasaki-Nomura in 2016, stating that a homogeneous cone of rank <i>r </i>is an irreducible symmetric cone if and only if the basic relative invariants of the cone and of the dual cone both have the degrees 1<i>, </i>2<i>......>, up to permutations. Our proof is based on the multiplier matrix of homogeneous cones studied in detail by the present author.</p>
- 件名homogeneous cones symmetric cones basic relative invariants
- 参照Characterizations of symmetric cones by means of the basic relative invariants of homogeneous cones Positive Riesz......on homogeneous cones REALIZATION OF HOMOGENEOUS CONES THROUGH ORIENTED GRAPHS A CHARACTERIZATION OF SYMMETRIC CONES BY THE DEGREES OF BASIC RELATIVE INVARIANTS
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