Jordan Canonical Form Calculation In MatLab®

Linear algebra is a very important area of calculus and linear algebra rules are used in engineering generally. Jordan canonical forms of matrices are also calculated in linear algebra. Matlab® provides a very useful command to calculate the Jordan canonical forms of matrices. This command is called ‘jordan()’. 

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Here we explain the use of the ‘jordan()’ command in Matlab® with a very basic example. You can also try this code example related to the ‘jordan()’ command in your Matlab® software. 

How To Use The ‘jordan()’ Command In MatLab®?

>> x = [1 -3 -2; -1 1 -1; 2 4 5]
[a, b] = jordan(x)

x =

     1    -3    -2
    -1     1    -1
     2     4     5

a =

    -1     1    -1
    -1     0     0
     2     0     1

b =

     2     1     0
     0     2     0
     0     0     3


As you see above, the use of the ‘jordan()’ command is very simple in Matlab®. To illustrate it, we just created a 3×3 matrix called ‘x’. Then we assigned the ‘jordan()’ command to two variables ‘a’ and ‘b’. This means we will see two results in the command window. 

We typed the matrix ‘x’ inside the parentheses of the ‘jordan()’ command. When we executed the code, we get two results. In the example above, the first one is the matrix ‘x’ itself. 

The ‘a’ that appeared in the command window is the similarity transformation matrix to obtain the canonical form of ‘x’. And the ‘b’ is the canonical form of the matrix ‘x’. 


As you see above, the use of the ‘jordan()’ command in Matlab® to obtain canonical forms of matrices is very simple. 

Do not forget to leave your comments and questions below about the use of the ‘jordan()’ command in Matlab® below. 

If you want further coding examples about the ‘jordan()’ command in Matlab®, inform us in the comments.

This article is prepared for completely educative and informative purposes. Images used courtesy of Matlab®

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