me is nonexistent or not a directory: G:\Bif To get started, type one of these: helpwin, helpdesk, or demo. To get color output on the HP DeskJet or Tek Phaser printers you MUST use the respective DESKJET and TEKPRINT m files For more information type "help deskjet" or "help tekprint" For product information, type tour or visit www.mathworks.com. >> a1 = [1 -1 0]' a1 = 1 -1 0 >> a2 = [2 0 -2]' a2 = 2 0 -2 >> a3 = [3 -3 3]' a3 = 3 -3 3 >> A = [a1 a2 a3] A = 1 2 3 -1 0 -3 0 -2 3 >> rref(A) ans = 1 0 0 0 1 0 0 0 1 >> A(2,:) = A(2,:) + A(1,:) A = 1 2 3 0 2 0 0 -2 3 >> A(3,:) = A(3,:) + A(2,:) A = 1 2 3 0 2 0 0 0 3 >> cd a:\Tcodes >> [l,u]=slu([a1 a2 a3]) l = 1 0 0 -1 1 0 0 -1 1 u = 1 2 3 0 2 0 0 0 3 >> [l,u]=lu([a1 a2 a3]) l = 1 0 0 -1 1 0 0 -1 1 u = 1 2 3 0 2 0 0 0 3 >> [l,u]=lu([1 2 3; -2 1 0; 5 1 2]) l = 0.2000 1.0000 0 -0.4000 0.7778 1.0000 1.0000 0 0 u = 5.0000 1.0000 2.0000 0 1.8000 2.6000 0 0 -1.2222 >> [l,u]=slu([1 2 3; -2 1 0; 5 1 2]) l = 1.0000 0 0 -2.0000 1.0000 0 5.0000 -1.8000 1.0000 u = 1.0000 2.0000 3.0000 0 5.0000 6.0000 0 0 -2.2000 >> help grams grams Gram-Schmidt orthogonalization of the columns of A. The columns of A are assumed to be linearly independent. Q = grams(A) returns an m by n matrix Q whose columns are an orthonormal basis for the column space of A. [Q, R] = grams(A) returns a matrix Q with orthonormal columns and an invertible upper triangular matrix R so that A = Q*R. Warning: For a more stable algorithm, use [Q, R] = qr(A, 0) . >> Q=grams([a1 a2 a3]) Q = 0.7071 0.4082 0.5774 -0.7071 0.4082 0.5774 0 -0.8165 0.5774 >> Q'*Q ans = 1.0000 0 0 0 1.0000 0 0 0 1.0000 >> Q(1,:) ans = 0.7071 0.4082 0.5774 >> Q(:,1) ans = 0.7071 -0.7071 0 >> Q(:,1)'*Q(:,1) ans = 1.0000 >> Q(:,2)'*Q(:,1) ans = 0 >> Q(:,3)'*Q(:,1) ans = 0 >> Q'*Q ans = 1.0000 0 0 0 1.0000 0 0 0 1.0000 >> [Q, R] = grams([a1 a2 a3]) Q = 0.7071 0.4082 0.5774 -0.7071 0.4082 0.5774 0 -0.8165 0.5774 R = 1.4142 1.4142 4.2426 0 2.4495 -2.4495 0 0 1.7321 >> help det DET Determinant. DET(X) is the determinant of the square matrix X. Use COND instead of DET to test for matrix singularity. See also COND. Overloaded methods help sym/det.m >> det([1 2;3 4]) ans = -2 >> det([1 2 3;4 5 6;7 8 9]) ans = 0 >> det([1 2 3 4 5;6 7 8 9 10;11 12 13 14 15;16 17 18 19 20;21 22 23 24 25]) ans = 0 >> rref([1 2 3 4 5;6 7 8 9 10;11 12 13 14 15;16 17 18 19 20;21 22 23 24 25]) ans = 1 0 -1 -2 -3 0 1 2 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 >> rref([1 2 3;4 5 6;7 8 9]) ans = 1 0 -1 0 1 2 0 0 0 >> help eig EIG Eigenvalues and eigenvectors. E = EIG(X) is a vector containing the eigenvalues of a square matrix X. [V,D] = EIG(X) produces a diagonal matrix D of eigenvalues and a full matrix V whose columns are the corresponding eigenvectors so that X*V = V*D. [V,D] = EIG(X,'nobalance') performs the computation with balancing disabled, which sometimes gives more accurate results for certain problems with unusual scaling. E = EIG(A,B) is a vector containing the generalized eigenvalues of square matrices A and B. [V,D] = EIG(A,B) produces a diagonal matrix D of generalized eigenvalues and a full matrix V whose columns are the corresponding eigenvectors so that A*V = B*V*D. See also CONDEIG, EIGS. Overloaded methods help sym/eig.m help lti/eig.m >> E=eig([1 2 3;4 5 6;7 8 9]) E = 16.1168 -1.1168 -0.0000 >> E=eig(sym([1 2 3;4 5 6;7 8 9])) E = [ 0] [ 15/2+3/2*33^(1/2)] [ 15/2-3/2*33^(1/2)] >> format long >> E=eig([1 2 3;4 5 6;7 8 9]) E = 16.11684396980706 -1.11684396980705 -0.00000000000000 >> format short >> E=eig([1 2 3;4 5 6;7 8 9]) E = 16.1168 -1.1168 -0.0000 >>