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396 APPENDICES
Description µ-Tools Function Xmath/Xµ equivalent
peak norm pkvnorm norm, max
absolute value vabs abs
diagonal matrix vdiag diagonal
round downwards vfloor round
round upwards vceil round
imaginary part vimag imag
real part vreal real
complex conjugate vconj conj
norm vnorm norm
determinant vdet det
eigenvalues veig eig
inverse vinv or minv inv
left division vldiv \
right division vrdiv /
pseudo-inverse vpinv pinv
spectral radius vrho spectrad
singular values vsvd svd
condition number vrcond rcond or condition
schur decomposition vschur schur
matrix exponential vexpm expm
interpolation vinterp interp or interpolate
decimation vdcmate pdm(vector)
FFT vfft fft
inverse FFT vifft ifft
spectral analysis vspectrum spectrum
Beware of syntactical differences here. One obvious example is the order in which the
eigenvalues and eigenvectors are returned from veig and eig. Note also the vrcond
returns the inverse of the condition number whereas condition returns the condition
number.
The µ-Tools function vebe performs element-by-element function operations on a
varying matrix. This has no counterpart in Xµ as the basic functions which operate on
each element of a matrix (e.g. sin, cos, abs) are also defined on pdms in Xmath. For the
same reason, the µ-Tools function veval has no Xµ counterpart: the Xmath execute
command can be used to the same effect.