 3
Matrices and Vectors
3.1 Overview
Both MATLAB and R can work directly with vectors and with m × n matrices (with the
usual convention that m speciﬁes the number of rows and n the number of co lumns). Both
platforms support vectorized computations, i.e., expressions that implicitly operate on entire
vectors or matrices. However, there a re some important diﬀerences between the two.
A key diﬀerence in syntax is that R uses square brackets to delimit matrix s ubscripts
(e.g., A[2,3]), while MATLAB uses parentheses (e.g., A(2,3)). R’s syntax has the ad-
vantage here because when reading MATLAB code, it is not immediately apparent
whether g(2,3) is accessing an element of a matrix g, or calling a function g with two
parameters.
In R, a vector is a primitive data type , and a matrix (which is actually a special case of
an array) is another distinct type. A vector with n elements is neither a row vector nor
a column vector, but simply an ordered set of n values. Care must sometimes b e taken
to ensure that a value is stored as a vecto r or matrix in particular .
In MATLAB, the fundamental data type is a matrix. A scalar value is simply a 1 × 1
matrix, while a vector with n elements is either an n × 1 matrix (column vector) or a
1 × n matrix (row vector). Care must sometimes be taken to ensure that a vector is a
row vector or a column vector in particular.
In R, you can use array subscripting on expressions. For example, to a c cess the element
in row 1, column 2 of the matrix A
2
, you can do ( A%*%A)[1,2]. You cannot perform
the corresp onding command (A*A)(1,2) in MATLAB. The easiest way around this is
to use a temporary variable, e.g., tmp=A*A; tmp(1, 2), although there is another way
(see Sec tion 3.9).
3.2 Creating vectors
In R, a vector is an ordered s e quence of values; it is neither a row vector nor a column
vector. In MATLAB, a vector is simply a special ca se of a matrix which has either one row
or one column.
Below a re many of the common ways of creating vectors.
1. Create a vector containing the spe ciﬁed values 4, 8, 15, 16, 23, 42
19 20 R and MATLAB
R MATLAB
c(4,8,15,16,23,42)
Or you can call sca n(), then enter the
values separated by spaces, and pres s
Return/Enter twice to signal the end of
the values. To explicitly construct a row
vector (s tored as a matrix), use
cbind(4,8,15,16,23,42); for a column
vector, use rbind(4,8,15,16,23,42).
Either [4,8,15,16,23,42] or [4 8 15
16 23 42] for a row vector. For a column
vector, [4;8;15;16;23;42] or
[4
8
15
16
23
42]
(R): The often-used function c combines” its arguments; it can work with many data
types.
(MATLAB): When entering matrices, co mmas or spaces can be used as delimiters be-
tween columns. Semicolons or newlines can be used between rows.
2. Vector of length k containing all zeros
rep(0,k) or numeric(k) zeros(k,1) (for column vector) or
zeros(1,k) (for row vector)
3. Vector of length k containing the value j in all positions
rep(j,k) j*ones(k,1) or repmat(j,k,1) (for
column vector); j*ones(1,k) or
repmat(j,1,k) (for row vector)
(R): rep is a widely used function which replicates its argument. It c an work with various
data types, and can be used in a few diﬀerent ways with vectors.
(MATLAB): repmat is used to replicate a matrix; because a scalar is simply a 1 × 1
matrix, it can also be use d as above.
4. Sequence with unit increment: 7, 8, 9, 10, 11
7:11 7:11 (for row vector), or (7:11)' (for
column vector).
(MATLAB): The apostrophe tr ansposes a matrix (but see entries 66 and 67 ), and can
also b e used to produce column vectors instead of row vectors for the entries below.
5. Values j 1 through k + 1 w ith unit increment
(j-1):(k+1) j-1:k+1
The fact that the colon has higher order of precedence than arithmetic operators in R
but not in MATLAB is a major nuisance. I have seen many people struggle to ﬁnd why
their code is broken, only for it to be caused by this issue. In R, writing j-1:k+1 r eally
means j-(1:k)+1 which is almost never what was intended. To be extra-cautious, I suggest
always using parentheses when wr iting expressions like this in either platform.
6. Sequence with increment -1: 11, 10, 9, 8, 7
11:7 11:-1:7
If you have gotten used to doing things like 11:7 in R, be careful when using MATLAB,
because it produces an empty matrix, and does not display any warnings or explicit signs
of trouble.
7. Sequence with speciﬁed increment: 4, 7, 10, 13
seq(4,13,by=3) or simply seq(4 ,13,3) 4:3:13

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