In this tutorial, we explore matrices in R. They are two dimensional arrays and homogeneous i.e. they can hold a single type of data.

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Academy R Programming: Matrix

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All the material related to this course are available on our website
Scripts can be downloaded from GitHub
Videos can be viewed on our Youtube Channel

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➢ Create matrices
➢ Matrix Operations
➢ Combine matrices
➢ Index/Subset matrix
➢ Dissolve matrix

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A matrix is a rectangular array of data elements, arranged in rows and columns. Matrices in R are
homogeneous i.e. they can hold a single type of data. Matrix elements are indexed by specifying the
row and column index and the elements of a matrix can be filled by row or columns. In the first
section, we look at various methods of creating matrices in R.

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The easiest way to create a matrix in R is to use the function. Let us look at its
syntax:
data Data Elements of the matrix Integer/Numeric/Logical/Character
nrow Number of rows Integer
ncol Number of columns Integer
byrow Whether data should be filled by rows Logical
dimnames Names of rows and columns Character vector

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Now that we have understood the syntax of the function, let us create a simple
numeric matrix:

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In the previous example, we created a matrix of 3 rows where the data elements are filled by
columns. We need to specify either the number of or and R will automatically
calculate the other. The number of data elements should be equal to the product of number of
rows and columns, else R will return an warning message.

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We can follow some general rules to avoid the mistakes made in the
previous two examples:
● If the number of data elements are odd, both the number of rows
and columns must be odd and their product should equal the
number of data elements.
● If the number of data elements are even, either the number of
rows must be even or the number of columns must be even. In
certain cases, both of them must be even.

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Let us continue to explore the syntax of the function. Let us create two matrices, the data
elements of which are filled by rows in the first case, and columns in the second case.

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Either the number of rows or columns need to be specified and R will calculate the other one automatically. We create
two matrices below, the first one specified by rows and the second one by columns.

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If we want to specify the names of the rows and columns, we need to use a data structure called . Lists can
contain other data structures including other lists. They are heterogeneous i.e. they can contain different data types.
We will learn more about lists in the next unit. For now, let us learn to create a basic list. Lists in R can be created using
the function.

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Let us now create a list of row and column names and use it to name the rows and columns of a
matrix.

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Another method to create a matrix is to use the function. It is basically used to check or specify the dimensions
of a data structure. In case of matrices, it returns the number of rows and columns. Let us look at a few examples:

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In the below example, we use the function to change the dimension of the matrix.In the dim function, we need to
mention both the number of rows and columns using the function. We change the rows from 3 to 4 and the
columns from 4 to 3.

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In the below example, we use the function to change row from 2 to 6 and the columns from 6 to 2.

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Now that we have understood the function, let us use it to convert vectors to matrices. Below are a few examples:

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The last method that we will explore in this section is the function. It is used to coerce a
data structure to the type . Since the only other data structure that we have covered so far is
the vector, we will coerce a vector to type We will deal with other data structures as and
when we learn about them.

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Regardless of the data type of vector, all of them are coerced to a of dimension n x 1 i.e. they
will all have only one column.

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In this section, we will cover the following:
● Matrix Addition
● Matrix Subtraction
● Matrix Division
● Transpose of a Matrix
● Matrix Multiplication
● Inverse of a Matrix
The four basic operations of addition, subtraction, multiplication and division can be done by element
wise or with a scalar value. We will be looking at both cases. In the case of multiplication, we need to
compute the transpose of the matrix before we can do element wise multiplication.

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We can use the function to compute the transpose of a matrix.

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We need to follow the basic rules of matrix multiplication i.e. the number of columns in the first matrix
should be equal to the number of rows in the second matrix. Let us look at an example:

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The inverse of a matrix can be computed using the function.

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In this section, we will focus on appending vector to matrices and combining matrices. There are two
functions that can be used for this purpose:
●
●
will combine/append the data by columns while will do the same by rows. When you
use to combine two matrices, the number of columns must match and in case of , the
number of rows must match.

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In this section, we will learn to index/subset elements of a matrix. The operator can be used to index
the elements as we did in case of vectors but since matrices are two dimensional, we need to specify
both the row number and the column number. Below are a few examples:

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In an earlier section, we learnt how to name the rows and columns of a matrix. Let us see how these
names can be used to subset matrices.

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When you are using names of columns or rows for subsetting data from matrices, ensure that they
are enclosed in single or double quotes.

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We can use logical expressions to subset elements of a matrix.

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So far, we have learnt how to coerce a vector to a matrix. In this final section, we will learn to
coerce a matrix to a vector. We can use the following functions:
●
●

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● Matrices are two dimensional arrays.
● They are homogeneous i.e. they can hold single type of data.
● The easiest way to create a matrix is by using the function.
● The function can be used to specify the dimensions of a matrix.
● They can be indexed using or names of rows/columns.
● Out of range index returns error.
● Negative index drops row/column from the matrix.
● Use function for transpose and function for inverse of a matrix.
● and can be used to append vectors and combine matrices.
● Logical expressions can be used to subset matrices.

41. R2
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In the next module:
✓ Construct Lists
✓ Describe Lists
✓ Index/Subset List Elements
✓ Convert Lists

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