Signature of a quadratic form | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-06-15

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Quadratic_form


00:01:42 1 Introduction
00:09:20 2 History
00:10:22 3 Real quadratic forms
00:11:19 4 Definitions
00:21:41 4.1 Quadratic spaces
00:29:34 4.2 Generalization
00:32:10 4.3 Related concepts
00:32:47 5 Equivalence of forms
00:34:58 6 Geometric meaning
00:35:56 7 Integral quadratic forms
00:36:07 7.1 Historical use
00:36:18 7.2 Universal quadratic forms
00:38:25 8 See also
00:40:15 9 Notes
00:44:13 10 References
00:45:25 11 Further reading
00:47:51 12 External links
00:51:00 See also



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SUMMARY
=======
In mathematics, a quadratic form is a polynomial with terms all of degree two. For example, 

  
    
      
        4
        
          x
          
            2
          
        
        +
        2
        x
        y
        −
        3
        
          y
          
            2
          
        
      
    
    {\displaystyle 4x^{2}+2xy-3y^{2}}
  
is a quadratic form in the variables x and y. The coefficients usually belong to a fixed field K,
such as the real or complex numbers, and we speak of a quadratic form over K.
Quadratic forms occupy a central place in various branches of mathematics, including number theory, linear algebra, group theory (orthogonal group), differential geometry (Riemannian metric, second fundamental form), differential topology (intersection forms of four-manifolds), and Lie theory (the Killing form).
Quadratic forms are not to be confused with a quadratic equation which has only one variable and includes terms of degree two or less. A quadratic form is one case of the more general concept of homogeneous polynomials.