List of functions (sorted by category)

Advanced mathematical functions: Advanced mathematical functions including Airy, Bessel, Beta and Elliptic functions. Function list.
airy     - Airy function
besselh  - Bessel function 3rd kind 
besseli  - modified Bessel function 1st kind
besselj  - Bessel function 1st kind
bessely  - Bessel function 2nd kind
beta     - beta function 
erf      - error function
erfc     - complementary error function
erfcinv  - inverse complementary error function
erfcx    - scaled complementary error function
erfinv   - inverse error function
expint   - exponential integral function
gamma    - gamma function
gammainc - incomplete gamma function
gammaln  - natural logarithm of gamma function
psi      - psi function

Basic mathematical functions: Most commonly used mathematical functions. See also "Trigonometric functions ". Function list.
abs       - absolute value
angle     - phase angle of complex numbers 
ceil      - rounds towards +inf
conj      - conjugate complex
exp       - exponential function
factor    - generates a list of factors
factorial - n!
fix       - rounds towards 0
floor     - rounds towards -inf
gcd       - greatest common divisor
imag      - imaginary part
lcm       - least common multiple
log       - natural logarithm
log10     - base 10 logarithm
log2      - base 2 logarithm
max       - largest element
min       - smallest element
mod       - modulo
real      - real part
rem       - integer quotient and remainder
rot90     - 90 degree rotation of matrices
round     - rounds to nearest number
sign      - sign of matrix elements
sqrt      - square root function

Commands: Commands in the Console control to manage screen appearance and variables. Function list.
clc                 - clears screen
clear [item]        - deletes the specified 'item'
clear all           - deletes all definitions in this file
ink [expression]    - renders 'expression' as ink
mathml [expression] - renders 'expression' as mathml

Constants: Commonly used constants and parameters used by the execution engine. Function list.
nan - not-a-number
eps - machine precision
inf - infinity
pi  - pi

Digital signal processing: A set of DSP functions that target filter design, FFT, windowing and signal manipulation. Function list.
fft      - Fourier transform
ifft     - inverse Fourier transform
linspace - linearly sampled data
logspace - logarithmically sampled data

Functions of polynomials: Functions that generate or manipulate polynomials and functions that deal with the roots of polynomials. Function list.
conv  - convolution
poly  - polynomial with given roots
roots - roots of polynomials

Linear algebra: A set of functions that manipulate, build up and decompose real and complex matrices. Function list.
chol       - Cholesky decomposition
compan     - companion matrix
cond       - condition number using SVD
ctrans - complex conjugate transpose
det        - determinant of a matrix
diag       - diagonal matrix or diagonal of a matrix
diff       - differences
dot        - dot product
eig        - eigenvectors and eigenvalues
expm       - matrix exponential
horzcat    - horizontal matrix concatenation
inv        - matrix inverse
logm       - matrix logarithm
lud        - lu-decomposition of matrices
nnz        - total number of nonzero matrix elements
norm       - vector/matrix norm
pinv       - pseudoinverse
qr         - QR-decomposition
rank       - matrix rank
reshape    - reshapes matrix
size       - matrix size
sort       - sorts vectors and matrices
sqrtm      - square root of a square matrix
sum        - sum
svd        - singular value decomposition
trace      - matrix trace
transpose  - non-conjugate transpose
vertcat    - vertical matrix concatenation

Matrix operators: Unitary and binary matrix functions that generate new matrices. Function list.
all - all inputs are 0

Membership: Functions that check whether certain elements belong to a given class of objects. Function list.
isprime  - checks whether matrix elements are prime numbers
isreal   - checks whether a matrix is real
issorted - matrix is sorted

Relational operators: Functions (operators) to compare numbers and matrices. Function list.
eq - equal
ge - greater than or equal
le - less than or equal
lt - less than
ne - not equal

Special matrices: Often used special vectors and matrices. Function list.
eye       - generates identity matrix
hadamard  - Hadamard matrix
hankel    - Hankel matrix
hilb      - Hilbert matrix
invhilb   - inverse of Hilbert matrix
ones      - matrix of ones
pascal    - Pascal matrix
peaks     - matrices for demonstration purposes
perms     - all permutations
primes    - generates a list of prime numbers
rosser    - Rosser matrix
toeplitz  - Toeplitz matrix
vander    - Vandermonde matrix
wilkinson - Wilkinson matrix
zeros     - matrix of zeros

Statistics: Typical statistical functions. Function list.
cov      - covariance matrix
hist     - histogram
mean     - mean value
median   - median value
nchoosek - binomial coefficient
rand     - uniformly distributed pseudorandom numbers
randn    - normally distributed pseudorandom numbers
std      - standard deviation
var      - variance

Support functions: Functions to convert, manage folders, display variables and manage variables. Function list.
help - provides online help
who  - returns variables
whos - returns variables with additional information

Trigonometric functions: A set of trigonometric and hyperbolic functions commonly used in applications. Function list.
acos  - inverse cos function
acosh - inverse hyperbolic cos function
acot  - inverse cot function
acoth - inverse hyperbolic cot function
acsc  - inverse cosecant function
acsch - inverse hyperbolic cosecant function
asec  - inverse secant function
asech - inverse hyperbolic secant function
asin  - inverse sin function
asinh - inverse sinh function
atan  - inverse tan function
atan2 - atan2 function
atanh - inverse hyperbolic tan function
cos   - cos function
cosh  - hyperbolic cos function
cot   - cot function
coth  - hyperbolic cot function
csc   - cosecant function
csch  - hyperbolic cosecant function
sec   - secant function
sech  - hyperbolic secant function
sin   - sin function
sinc  - sinc function
sinh  - sinh function
tan   - tan function
tanh  - tanh function

Vector analysis: Functions that generate vectors based on given vectors or matrices. Function list.
cross - cross product
kron  - Kronecker tensor product