Exam 3 Flashcards
1
Q
Formula for diagonalizing a matrix
A
D = P^(-1)AP (D = P^(T)AP if orthogonal matrix)
2
Q
Inner product generated by a matrix
A
= UA^(T)AV^(T)
3
Q
Standard Inner product of square matrices
A
tr(U^(T)V)
4
Q
cos(x) =
A
u · v
5
Q
least squares solutions
A
A^(T)Ax = A^(T)b
6
Q
least squares error
A
||b - Ax||
7
Q
square matrix is orthogonal if
A
A^(T) = A^(-1)
8
Q
Cauchy-Schwartz
A
|u · v| <= ||u|| ||v||
9
Q
orthogonal projection of u on subspace spanned by vectors
A
A^(T)Ax = A^(T)b
10
Q
least squares straight line fit to points
A
M^(T)Mv = M^(T)y
