166 Appendix A: MATLAB commands continued

$\gg$B’ [computes the transpose $B^t$ of $B$]

$\gg$ rref(A) [finds the reduced echelon form of $A$]

$\gg$ rank(A) [finds the rank of $A$]

$\gg$poly(A) [finds the coefficients of the characteristic polynomial of square matrix A]

$\gg$eig(A) [finds the eigenvalues of square matrix $A$, in a list]

$\gg$ jordan(A) [finds the Jordan canonical form of $A$]

$\gg$[W,D]=eig(A) [gives a matrix W with columns that are eigenvectors of $A$ and diagonal matrix D]

$\gg$ A${}^2$ [computes the matrix product $A^2$]

$\gg$A.${}^2$ [creates matrix by squaring each entry of $A$; note dot]

$\gg$A*B [calculates the matrix product $AB$]

$\gg$expm(A) [calculates the matrix exponential of $A$]

$\gg$exp(A) [calculates the matrix formed by taking the exponential of each entry of $A$]

$\gg$syms x [introduces algebraic variable $x$]