1. Some useful linear algebra

2. Linearly independent vectors
span(V): span of vector space V is all linear combinations of vectors vi,i.e.

4. The eigenvalues of A are the roots of the
characteristic equation
diagonal form of matrix
Eigenvectors of A are columns of S

5. Similarity transform
then A and B have the same eigenvalues
The eigenvector x of A corresponds to the eigenvector
M-1x of B

6. Rank and Nullspace

7. Least Squares More equations than unknowns
Look for solution which minimizes ||Ax-b|| = (Ax-b)T(Ax-b)
Solve
Same as the solution to
LS solution

10. Properties of SVD si2 are eigenvalues of ATA
Columns of U (u1 , u2 , u3 ) are eigenvectors of AAT
Columns of V (v1 , v2 , v3 ) are eigenvectors of ATA

12. Solving pseudoinverse of A equal to for all nonzero singular
values and zero otherwise
with

13. Least squares solution of homogeneous equation Ax=0

14. Enforce orthonormality constraints on an estimated rotation matrix R’

15. Newton iteration
f( ) is nonlinear
parameter
measurement

16. Levenberg Marquardt iteration