If the matrix is not symmetric, then <u, v> != <v, u>. Therefore it can't be a well-defined inner product.
motoole2
As we covered last lecture, if the inner product of two vectors <u,v> represents the angle between them, then flipping the order of these vectors <v,u> should give the same answer. Back to this slide, the expression only makes sense if the matrix A is symmetric, since that is the only way to satisfy the property <u,v> = <v,u>.
If the matrix is not symmetric, then <u, v> != <v, u>. Therefore it can't be a well-defined inner product.
As we covered last lecture, if the inner product of two vectors
<u,v>represents the angle between them, then flipping the order of these vectors<v,u>should give the same answer. Back to this slide, the expression only makes sense if the matrixAis symmetric, since that is the only way to satisfy the property<u,v> = <v,u>.