Octave Programming Tutorial/Linear algebra

Functions

det(A) computes the determinant of the matrix A.
lambda = eig(A) returns the eigenvalues of A in the vector lambda, and
[V, lambda] = eig(A) also returns the eigenvectors in V but lambda is now a matrix whose diagonals contain the eigenvalues. This relationship holds true (within round off errors) A = V*lambda*inv(V).
inv(A) computes the inverse of non-singular matrix A. Note that calculating the inverse is often 'not' necessary. See the next two operators as examples. Note that in theory A*inv(A) should return the identity matrix, but in practice, there may be some round off errors so the result may not be exact.
A / B computes X such that $XB=A$ . This is called right division and is done without forming the inverse of B.
A \ B computes X such that $AX=B$ . This is called left division and is done without forming the inverse of A.
norm(A, p) computes the p-norm of the matrix (or vector) A. The second argument is optional with default value $p=2$ .
rank(A) computes the (numerical) rank of a matrix.
trace(A) computes the trace (sum of the diagonal elements) of A.
expm(A) computes the matrix exponential of a square matrix. This is defined as

I+A+{\frac {A^{2}}{2!}}+{\frac {A^{3}}{3!}}+\cdots

Below are some more linear algebra functions. Use help to find out more about them.

R = chol(A) computes the Cholesky factorization of the symmetric positive definite matrix A, i.e. the upper triangular matrix R such that $R^{T}R=A$ .
[L, U] = lu(A) computes the LU decomposition of A, i.e. L is lower triangular, U upper triangular and $A=LU$ .
[Q, R] = qr(A) computes the QR decomposition of A, i.e. Q is orthogonal, R is upper triangular and $A=QR$ .

Below are some more available factorizations. Use help to find out more about them.

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