Matrix Representation
Let be a basis for V. Define the n×n matrix A by . The matrix A is a symmetric matrix exactly due to symmetry of the bilinear form. If the n×1 matrix x represents a vector v with respect to this basis, and analogously, y represents w, then is given by :
Suppose C' is another basis for V, with : with S an invertible n×n matrix. Now the new matrix representation for the symmetric bilinear form is given by
Read more about this topic: Symmetric Bilinear Form
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