The Unapologetic Mathematician

Mathematics for the interested outsider

Bilinear Forms

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April 14, 2009 - Posted by | Algebra, Linear Algebra


  1. […] Inner Products Now that we’ve got bilinear forms, let’s focus in on when the base field is . We’ll also add the requirement that our […]

    Pingback by Real Inner Products « The Unapologetic Mathematician | April 15, 2009 | Reply

  2. […] Inner Products Now consider a complex vector space. We can define bilinear forms, and even ask that they be symmetric and nondegenerate. But there’s no way for such a form to […]

    Pingback by Complex Inner Products « The Unapologetic Mathematician | April 22, 2009 | Reply

  3. […] start with either a bilinear or a sesquilinear form on the vector space . Let’s also pick an arbitrary basis of . I want […]

    Pingback by Matrices and Forms I « The Unapologetic Mathematician | June 24, 2009 | Reply

  4. […] of matrices and forms and try to tie both views of our matrix together. We’re considering a bilinear form $ on a vector space over the real or complex numbers, which we can also think of as a linear […]

    Pingback by Matrices and Forms II « The Unapologetic Mathematician | June 25, 2009 | Reply

  5. […] back in on a real, finite-dimensional vector space and give it an inner product. As a symmetric bilinear form, the inner product provides us with an isomorphism . Now we can use functoriality to see what this […]

    Pingback by Tensor Algebras and Inner Products I « The Unapologetic Mathematician | October 29, 2009 | Reply

  6. […] I said above, this is a bilinear form. Further, Clairaut’s theorem tells us that it’s a symmetric form. Then the spectral […]

    Pingback by Classifying Critical Points « The Unapologetic Mathematician | November 24, 2009 | Reply

  7. […] this as a bilinear function which takes in two vectors and spits out a number . That is, is a bilinear form on the space of tangent vectors at […]

    Pingback by (Pseudo-)Riemannian Metrics « The Unapologetic Mathematician | September 20, 2011 | Reply

  8. […] the next three families of linear Lie algebras we equip our vector space with a bilinear form . We’re going to consider the endomorphisms such […]

    Pingback by Orthogonal and Symplectic Lie Algebras « The Unapologetic Mathematician | August 9, 2012 | Reply

  9. […] can now define a symmetric bilinear form on our Lie algebra by the […]

    Pingback by The Killing Form « The Unapologetic Mathematician | September 3, 2012 | Reply

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