Determinantとは 意味・読み方・使い方

語源

Borrowed from French déterminant, equivalent to determine +‎ -ant.

発音

• (英国発音, General Australian) IPA: /dɪˈtɜːmɪnənt/
• (General American, Canada) IPA: /dɪˈtɝmɪnənt/, /dɪˈtɝmənənt/

名詞

determinant (plural determinants)

1. A determining factor; an element that determines the nature of something.
   • 1999, Noah P. Barsky, Stuart Bruchey (editor), Organizational Determinants of Budgetary Influence and Involvement, Taylor & Francis (Garland Publishing), page 4,

     Shields and Young (1993) argue that the budget participation literature "has not produced a coherent nor unified definition" of both the determinants and consequences of budget participation.

   • 2003, Agis D. Tsouros, “Foreword”, in Richard Wilkinson, Michael Marmot, editors, Social Determinants of Health: The Solid Facts, 2nd edition, World Health Organization, page 5:

     The field of the social determinants of health is perhaps the most complex and challenging of all.

   • 2004, Carsten Anckar, Determinants of the Death Penalty: A comparative study of the world, Taylor & Francis (Routledge), page 165:

     The aim of this book has been to assess the determinants of capital punishment without taking a stand for or against the death penalty.

2. (linear algebra) A scalar that encodes certain characteristics of a given transformation matrix; the unique scalar function over square matrices which is distributive over matrix multiplication, multilinear in the rows and columns, and takes the value 1 for the unit matrix; abbreviated as: det.
   • 1966 [Allyn & Bacon], Howard Whitley Eves, Elementary Matrix Theory, 1980, Dover, Unabridged corrected republication, page 165,

     The determinant of a square matrix ${\displaystyle A_{(n)}}$ is a function (actually a polynomial function) of the elements ${\displaystyle a_{ij}}$ of ${\displaystyle A}$.

   • 1990, Assem S. Deif, Advanced Matrix Theory for Scientists and Engineers, Gordon and Breach Science Publishers (Abacus Press), 2nd Edition, page 18,

     Show that the determinant of a Hermitian matrix is real and that of a skew-Hermitian matrix is imaginary.

   • 2009, Richard A. Brualdi, Dragoš Cvetkoviċ, A Combinatorial Approach to Matrix Theory and Its Applications‎, Taylor & Francis (CRC / Chapman & Hall), page 63:

     Using this definition, we derive the basic properties of a determinant that are useful in its evaluation. In particular, it is shown how the calculation of a determinant can be reduced to the calculation of determinants of lower order.

   • 2019 June 24, Juan Triana, “Negafibonacci Numbers via Matrices”, in Bulletin of TICMI‎, volume 23, number 1, →ISSN, archived from the original on 2019-07-13, Negafibonacci numbers as tridiagonal matrix determinants, pages 3, 4:

     The following proposition shows a connection between negafibonacci numbers and the determinants of a family of tridiagonal matrices. […] Assuming that the determinant det(G_k) = f_−(k+1) for all k ≤ n, we aim to show that det(G_n+2) = f_−(n+3).

3. (biology) A substance that causes a cell to adopt a particular fate.
4. (genetics) Something that causes a nuclease to cut at a specified point

派生語

形容詞

determinant (comparative more determinant, superlative most determinant)

1. Serving to determine or limit; determinative.

派生語

参考

• permanent
• singular

参照

Further reading

• Risk factor on Wikipedia.Wikipedia
• Determinantal variety on Wikipedia.Wikipedia
• Determinant on Wolfram MathWorld
• Determinant on Encyclopedia of Mathematics

アナグラム

• detrainment