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welcome to video lecture f10 this one is on classifying quadratic forms Ill be your CEO thats chief Education Officer Tom Roby and here are the outlining objectives we want to apply the principal axis theorem that we saw in a recent video lecture to koala to classify quadratic forms based on their eigenvalues so it turns out that theres something roughly the sign of a quadratic form whether its positive definite negative definite indefinite or there a couple of other cases that well talk about this is determined by the sign of its eigenvalues a set of eigen multi set of eigen values is sometimes called the spectrum so if I use that terminology thats what I mean by it and thats all well try to do in this video lecture lets take a look at some pictures to help us understand whats going on right away so pictured below are graphs of three quadratic forms and I cant point at them very well because notice that thats okay ik to my finger and the rest of me so but if you look you