MATLAB Reference Card
Note: This reference card gives only a short summary. For detailed syntax
and behavior, see the MATLAB help.1
Getting help
All MATLAB functions have online documentation.
help <command> Help on <command>
doc <command> Detailed documentation on <command> (opens in help
browser).
Workspace
who displays a list of variables in the workspace
whos displays a detailed list of variables in the workspace
format sets the default format how MATLAB displays numbers.
format short 5 digit fixed point
format long 15 digit fixed point
format short e 5 digit floating point
format long e 15 digit floating point
clear x clears the variable x
clear erases all variables in the workspace
clc clears the command window
close n closes figure window no. n
close all closes all figure windows
... Three or more periods at the end of a line continue the current command
or function call onto the next line. Text on a line after ... is ignored. (Un-
like C or Java, in MATLAB a command is normally terminated by a newline
character.)
Data Creation
x=[1,2,4,...] define a row vector x
x=[1 2 4 ...] same.
x=[1; 2; 5; ...] define a column vector x
a:c the range a..c; equivalent to [a,a+1,...,c-1,c]
a:b:c the range a..c with step size b; equivalent to [a,a+b,a+2*b,...,
c-b,c]
linspace(a,b,n) a row vector with nvalues linearly spaced from ato b
(inclusive)
eye(n) the n×nidentity matrix
zeros(n) an×nzero matrix
zeros(m,n) am×nzero matrix
ones(n) an×nall-one matrix
ones(m,n) am×nall-one matrix
diag(x) creates a diagonal matrix whose diagonal consists of the entries of
the vector x
[X,Y]=meshgrid(x,y) transforms the domain specified by vectors x
and yinto matrices Xand Ythat can be used for the evaluation of functions of
two variables.
Slicing and Extracting Data
Indexing vectors
x(1) 1st element
x(n) nth element
x(end) last element
x(1:n) first nelements
x(end-n:end) last n+1 elements
x([1 2 4]) specific elements (use any row or column vector as index)
x(x>3) all elements greater than 3
x(x>3 & x<5) all elements between 3 and 5
x(:) transformed to column vector
Indexing matrices
x(i,j) element at row i, column j
x(i,:) row i
x(:,j) column j
x(1:m,:) first nrows
x(:,1:n) first ncolumns
x(end,end) The last element in the last row
x(:) transformed to column vector (column by column)
Variable Information
length(a) the length of the vector x. For matrices length returns the
number of rows or columns, whichever is larger.
[x,y]=size(a) the number of rows (x) and columns (y) of the matrix a
size(a,1) the number of rows of a
size(a,2) the number of columns of a
numel(a) the number of elements in a
nnz(a) the number of non-zero elements in a
Data Selection and Manipulation
x’ the complex conjugate transpose of x
x.’ the non-conjugate transpose of x
2max(x) the greatest element of x
2min(x) the smallest element of x
2fliplr(x) reverses the elements of xfrom left to right
2flipud(x) reverses the elements of xfrom top to bottom
2[a,i]=max(x) returns in addition the position iof the greatest element
2[a,i]=min(x) returns in addition the position iof the smallest element
2sort(x) sorts the elements of xin ascending order
2sortrows(x) sorts the rows of xin ascending order as a group, according
to the first column.
2sortrows(x,c) as above, but sorted according to column c. If cis neg-
ative, the rows are sorted by descending order. If cis a vector, the rows are
sorted first by column c(1), then by column c(2), etc.
find(x) returns the indices corresponding to the nonzero entries of x
find(x==a) returns the indices of the positions jsuch that x[j]==a[j]
unique(x) returns the same values as in abut with no repetitions; the val-
ues will also be sorted.
reshape(x,m,n) returns the m×nmatrix whose elements are taken
columnwise from x.
Matrix Computations
a+b If aand bare m×nmatrices, this is the standard matrix addition. If ais
a matrix and bis a scalar, or vice-versa, the scalar is added to every entry of
the matrix.
a-b If aand bare m×nmatrices, this is the standard matrix subtraction. If a
is a matrix and bis a scalar, or vice-versa, the scalar is subtracted from every
entry of the matrix.
a*bIf ais an k×mmatrix and bis an m×nmatrix, this is the standard
matrix multiplication, i.e., yielding an k×nmatrix. If ais a matrix and bis a
scalar, or vice-versa, every element of the matrix is multiplied by the scalar.
a.*bIf aand bare m×nmatrices, this is their pointwise multiplication. If
either element is a scalar, this is the same as a*b.
a/b If aand bare matrices of appropriate dimensions, this is roughly
a*inv(b). If bis a scalar, this divides every entry of aby b.
a./b If aand bare m×nmatrices, this is their pointwise division. If ais a
scalar, then this divides aby every entry of b. If bis a scalar, then this divides
every entry of aby b.
a\bIf ais an n×nmatrix and bis an n×1 column vector, or a matrix with
several such columns, then x=a\bis the solution to the equation a*x=b. If a
is a scalar, then this divides every entry of bby a.
a.\bIf aand bare m×nmatrices, this is their left pointwise division. If a
is a scalar, then this divides every entry of bby a. If bis a scalar, then this
divides bby every entry of a.
a’*bIf aand bare n×1 column vectors, this is their inner product (or scalar
product or dot product). (This is not another operator, just a combination of ’
(conjugate transpose) and *).
inv(a) The inverse of the n×nmatrix a.
eig(a) is a vector containing the eigenvalues of the n×nmatrix a.
[v,d]=eig(a) produces a diagonal matrix dof eigenvalues and a full ma-
trix vwhose columns are the corresponding eigenvectors such that a*v=v*d.
rank(a) is the rank, or number of linearly independent rows or columns of
the matrix a.
Math
sin,cos,tan,asin,acos,atan,atan2,log,log10,exp,...
These are the standard mathematical functions; they always operate point-
wise on their arguments.
sum(x) sum of the elements of x
prod(x) product of the elements of x
diff(x) difference (and sample-wise derivative) of the vector x
cumsum(x) cumulative sum of the elements of x(and sample-wise integral)
cumprod(x) same, for the product
mean(x) mean of the elements of x
median(x) median of the elements of x
log(x, base) computes the logarithm of xwith base base
real(x) real part of a complex number
imag(x) imaginary part of a complex number
abs(x) absolute value of x, or complex magnitude if xis a complex number
angle(x) angle in radians of the complex number
conj(x) the complex conjugate of x
1Based on the R Reference Card by Tom Short, [email protected].
2For Matrices, these commands work columnwise.
