Why do i get the error (Array indices must be positive integers or logical values) when trying to calculate the determinant

Hi @BICU,

You have a matrix data that you transpose into datat. From this transposed matrix, you extract specific elements (r3 and r2) to compute a new vector P1. Then, you create a diagonal matrix M from this vector and compute its determinant using MATLAB's det() function.

https://www.mathworks.com/help/matlab/ref/det.html

You seek clarification on whether the determinant calculated (det = 1.3971e+03) is accurate or if there is an error in your approach. Please see attached.

Let me help you understand by breaking down your code.

Data Initialization

   data = [
       3.88,  0.54, 2.34,  3.00;
       18.00, 4.60, 5.20,  6.00;
       23.00, 4.00, 7.40, -2.00
   ];
   datat = data';

This creates a transposed matrix where the rows become columns.

Extracting Values

   r3 = datat(3,2); % This retrieves the element at row 3, column 2
   r2 = datat(2,:); % This retrieves the entire second row

Here, r3 is assigned the value 5.20, and r2 becomes a row vector [0.54, 4.60, 4.00]

Calculating P1

   P1 = r3 * r2; % Multiplying scalar r3 with row vector r2

The result is a row vector: P1 = [5.20 times 0.54, 5.20 times 4.60, 5.20 times 4.00] = [2.8080, 23.9200, 20.8000]

Creating Diagonal Matrix

   M = diag(P1); % Constructs a diagonal matrix from P1

Calculating Determinant

   det = det(M); % Computes the determinant of the diagonal matrix M

For a diagonal matrix M constructed from vector P1, the determinant can be calculated as the product of its diagonal elements:

 de(M) = P1 times P1(2) times P1(3) = 2.8080 times 23.9200 times 20.8000

This multiplication indeed yields approximately 1.3971e+03 confirming that your calculation is accurate. Your code correctly computes the determinant of the diagonal matrix derived from P1. The output you received (det = 1.3971e+03) is indeed correct based on your calculations. If you noted in the Matrix documentation provided, while determinants can give insights into matrix properties (like singularity), they can be sensitive to numerical errors and should not be relied upon solely for determining singularity or conditioning of matrices. If you are concerned about singularity or numerical stability in matrices in future applications, consider using functions like cond() or rcond() for more reliable assessments.

https://www.mathworks.com/help/symbolic/sym.cond.html?searchHighlight=cond&s_tid=srchtitle_support_results_2_cond

https://www.mathworks.com/help/matlab/ref/rcond.html?s_tid=doc_ta

This thorough breakdown should clarify any doubts regarding your MATLAB code and the accuracy of the determinant computed therein!

Hope this helps.