2.2 Constructing a diagonal matrix

In some cases we may want to construct a diagonal matrix. The function diag is available for this. diag may be used in several ways. If a single scalar input n is supplied then the $n\times n$ identity matrix ${𝐈}_n$ is created. For instance

I <- diag(10)

creates a $10\times 10$ identity matrix. If two scalar inputs k and n are supplied then the $n\times n$ matrix $k{𝐈}_n$ is created, e.g.

I <- diag(5,7)

creates a $7\times 7$ matrix with diagonal elements 5. If a single vector input is supplied then a diagonal matrix with diagonal elements corresponding to the elements of that vector is created e.g.

H <- diag(c(1,2,3,4))

creates the matrix

In the next section we will see that diag can also be used to extract the diagonal elements of a matrix.

 

Workshop 1: Constructing a matrix (I)

Construct a matrix

 

 

Workshop 2: Constructing a matrix (II)

Construct a $10\times 10$ matrix of the form:

 

 

Quiz 1: Constructing a matrix (III)

Which of the following commands creates the matrix

1. (A)

   matrix((2:74),5,5,byrow=TRUE)

2. (B)

   matrix(3*(1:25) - 1, 5,5,byrow=TRUE)

3. (C)

   matrix(rep(2:74,3),5,5,byrow=TRUE)

4. (D)

   matrix(rep(c(2,17,32,47,62),5),5,5,byrow=FALSE)

5. (E)

   matrix(seq(2,74,by=3),5,5,byrow=FALSE)