EUCLIDEAN QUADRATIC FORMS ARE ADC FORMS a SHORT Math Uga

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in this video we're going to be talking about quadratic forms so far we've mostly looked at systems of linear equations things of the form some matrix a times x equals some vector B we call these things systems of linear equations because for each of these equations the degrees of the variables are at most one for example let's look at the matrix equation one two three four times x equals the vector five six this here can be thought of as a system of equations where we have X 1 plus 2 X 2 equals 5 + 3 X 1 plus 4 X 2 equals 6 again these are linear equations because the degrees of the variables X 1 and X 2 are at most 1 on the other hand a quadratic form is a polynomial in n variables where the terms are all degree 2 let's look at some examples of quadratic forms so let Q 1 be the polynomial x 1 squared this is a quadratic form in one variable and here I have the X 1 and its squared so it's degree 2 let Q 2 be the polynomial x1 squared plus x2 squared this is a quadratic form in two var