linsolve(A,b): solve linear system Ax = b using LU decomposition
with partial pivoting (for square matrix), otherwise QR factorization
lu(A):
LU decomposition with pivoting, {L U] = lu(A) returns L, U so that A =
L*U, but L is permuted lower triangular; [L U P] = lu(A) will return L,
U, and P so that P*A = L*U.
null(A):
orthonormal basis for null space of A, i.e. {x: Ax = 0}
orth(A):
orthonormal basis for columnspace of A, use orth(A, 'r') to get a
rational basis
qr(A,0):
economy QR factorization, i.e. A = QR with Q orthonormal (Q'*Q = I), R
upper triangular; if A = mxn, then Q = mxn, and R = nxn. In the full
factorization, [Q R] = qr(A), Q has dimension mxm.
eig(A):
eigenvalues of A, if used as [P D] = eig(A), P contains eigenvectors and
D is diagonal matrix of corresponding eigenvalues; in particular, A =
P*D*P^(-1).
svd(A):
singular value decomposition; use as [U D V] = svd(A), then A = PDV'
Images
imread(name):
read file with name; format is based on extension of file name
imwrite(pic,name):
write picture data in pic to file name
im2double(pic):
convert image information to double precision
rgb2grayscale(pic): convert color picture to grayscale picture, loses
color information