Tartalomjegyzék

Matlab brochure

Built-in linear algebra Matlab functions:

Q = orth(A) - Gives an orthonormal basis of the image space of a matrix
Z = null(A) - Returns an orthonormal basis for the null space of A
[U,S,V] = svd(A) - Singluar value decomposition of matrix A (see also Fundamental theorem of linear algebra)
k = rank(A,) - Rank of matrix A
[R,p] = rref(A) - Reduced row echelon form (Gauss-Jordan elimination). p gives the indices of the first k nr of linearly independent rows of matrix A, where k = rank(A)
[r,p,k] = residue(b,a); [b,a] = residue(r,p,k) - Partial fractional decomposition (numerical)
poly - Polynomial with specified roots or characteristic polynomial
polyval - Polynomial evaluation
roots - Polynomial roots
w = conv(u,v) - Convolution and polynomial multiplication
[q,r] = deconv(u,v) - Deconvolution and polynomial division

Built-in Matlab functions:

subexpr
subs(expr) - it can be used only with a single argument as well
simplifyFraction
compose
combine(sin(x)+cos(x),'sincos')
divisors - divisors of a polynomial
factor - FactorMode: real/complex/full/rational
partfrac - FactorMode: real/complex/full/rational
rewrite(csc(x),'sin') or rewrite(asinh(x),'log') - sin, cos, sincos, tan, exp, log, heaviside, sqrt
isAlways - prove a statement
in(.., type) - types: real, positive, integer, rational
minpoly
charpoly - characteristic polynomial of a matrix
symsum(i,[1,n]) - $\displaystyle\sum_{i = 1}^n i = \frac{n(n+1)}{2}$

Optimization

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