Linear Algebra Essentials

Linear Algebrabeginner~8 min

Solve linear systems, compute eigenvalues, and perform matrix decompositions.

Step 1 — Create and manipulate matrices

Use square brackets with semicolons for row separators.

A = [1 2 3; 4 5 6; 7 8 10];
size(A)
det(A)

Expected output: Matrix size [3, 3] and determinant = -3

solve(A, b) solves linear systems using LU decomposition. This is SimLab's equivalent of MATLAB's A\b.

A = [2 1; 5 3];
b = [4; 7];
x = solve(A, b)

Expected output: x = [5; -6]

eig(A) returns eigenvalues. Eigenvalues reveal natural frequencies, stability, and system modes.

A = [4 1; 2 3];
d = eig(A);
disp(d)

Expected output: Eigenvalues: [5, 2]

Singular Value Decomposition reveals rank, condition, and principal components.

A = [1 2; 3 4; 5 6];
[U, S, V] = svd(A);
disp(S)

Expected output: Singular values showing matrix rank