Symmetric Matrices and Positive Definiteness

[@magicandmagik]

He is actually using the more formal definition of positive definite matrices, which is that for any x, (x bar transpose) * A * x must be greater than zero this definition isn't taught in the lecture but it is good to know.

[@xXasd012xX]

thanks, you saved me a lot of time

[@quirkyquester]

Thank you so much!

[@ysmashimaro]

3:49 Why does a projection matrix's eigenvalues are either 0 or 1?

[@RC98.19]

It's easy to find an explanation! math.stackexchange.com/questions/1157589/find-the-eigenvalues-of-a-projection-operator

[@quirkyquester]

@@RC98.19 Thank youuuuu!!!!!

[@divykala169]

Intuitively, if a vector X lies in the plane to which the projection matrix projects, PX = 1X. If the vector X is normal to the plane onto which the projection matrix projects, then PX = 0X.

[@turokg1578]

@@RC98.19 thx

[@garethcheung]

Why are symmetric matrices always diagonalizable?

[@sipraneye70]

cuz u can always find linearly independent n perpendicular eigenvectors to the eigenvalues n construct a matrix consisting of all the eigenvectors

[@magicbanana3393]

Part A possible alternate solution? A is positive definite and every positive definite matrix has all positive eigenvalues If det(A) = 0 then 0 is an eigenvalue of the matrix, but this is a contradiction because positive definite matrix must have positive eigenvalues. This shows det(A) is non-zero.

[@All_Kraft]

Why if P is projection then eig 0,1?

[@danicarovo8818]

Help, every time he says "detA" I hear "daddEY", then he started with "detS" and all i hear "datAss"☠️