MATLAB is a powerful numerical computing environment that can easily create and manipulate matrices. Creating a diagonal matrix, in particular, is a common task in MATLAB and can often be used to solve linear algebra problems. This guide will provide you with a step-by-step explanation on how to create a diagonal matrix in MATLAB.

## Step 1: Define the Non-Zero Diagonal Elements

First, we need to define the sizes of the matrix, as well as the non-zero diagonal elements. This can be done by inputting a singleton vector, which is a vector with only one element, into the `diag`

function. The input syntax of `diag`

is `diag(singletonVector)`

, and the matrix it creates is (size of `singletonVector`

) by (size of `singletonVector`

).

For example, if you wanted to generate a 3 x 3 matrix with the diagonal elements of 4, 5, and 6, you would use the singleton vector `[4, 5, 6]`

with the following syntax: `diag([4, 5, 6])`

. This will create the following matrix:

$$

\begin{bmatrix}

4 & 0 & 0 \

0 & 5 & 0 \

0 & 0 & 6

\end{bmatrix}

$$

## Step 2: Define the Entire Matrix

Using the same syntax, you can define the entire matrix as well. This can be done by inputting a matrix instead of a singleton vector. For example, if you wanted to generate a 3 x 3 matrix with the diagonal elements of 4, 5, and 6, and the off-diagonals of 1, 2, and 3, you would use the input `[4, 1, 2; 1, 5, 3; 2, 3, 6]`

with the following syntax: `diag([4, 1, 2; 1, 5, 3; 2, 3, 6])`

. This will create the following matrix:

$$

\begin{bmatrix}

4 & 1 & 2 \

1 & 5 & 3 \

2 & 3 & 6

\end{bmatrix}

$$

## Step 3: Define a Lower- or Upper-Triangular Matrix

You can also use `diag`

to create a lower- or upper-triangular matrix. This can be done by inputting a matrix that only has values in the on the lower- or upper-triangle. For example, if you wanted to generate a 3 x 3 lower-triangular matrix with the diagonal elements of 4, 5, and 6, and the off-diagonals of 1, 2, and 3, you would use the input `[4, 0, 0; 1, 5, 0; 2, 3, 6]`

with the following syntax: `diag([4, 0, 0; 1, 5, 0; 2, 3, 6])`

. This will create the following matrix:

$$

\begin{bmatrix}

4 & 0 & 0 \

1 & 5 & 0 \

2 & 3 & 6

\end{bmatrix}

$$

## FAQ

#### What is a diagonal matrix?

A diagonal matrix is a matrix where the values are only on the diagonals and all other elements are zero.

#### What is the syntax for creating a diagonal matrix in MATLAB?

The syntax for creating a diagonal matrix in MATLAB is `diag(vector)`

, such as `diag([4, 5, 6])`

. You can also input a matrix instead of a singleton vector if you want to define the off-diagonal elements.

#### Can I create a lower- or upper-triangular matrix using `diag`

?

Yes, you can create a lower- or upper-triangular matrix using `diag`

by inputting a matrix that only has values on the lower- or upper-triangle.

#### What is the syntax for creating a lower-triangular matrix in MATLAB?

The syntax for creating a lower-triangular matrix in MATLAB is `diag(matrix)`

, such as `diag([4, 0, 0; 1, 5, 0; 2, 3, 6])`

.

#### Can I use `diag`

for vectors of different sizes?

Yes, you can use `diag`

for vectors of different sizes by changing the length of the singleton vector or matrix. The resulting matrix will then be (length of vector/matrix) by (length of vector/matrix).