how to calculate the left kernel of a matrix in matlab

To calculate the left kernel of a matrix in Matlab, you can use the null function. The null function calculates a basis for the null space of a matrix, which is the left kernel of the matrix.

Here's an example code:

main.m
% Define matrix A
A = [1, 2, 3;
     4, 5, 6;
     7, 8, 9];

% Calculate the left kernel of A
left_kernel = null(A', 'r');

% Display the result
disp('Left kernel of A:');
disp(left_kernel);
192 chars
12 lines

In this code, we first define a matrix A. We then calculate the left kernel of A by calling null(A', 'r'). The 'r' argument specifies that we want to compute a rational basis for the null space. Finally, we display the left kernel of A using disp(left_kernel).

Note that we need to transpose the matrix A to calculate its left kernel. This is because the null function calculates the right kernel of its input matrix. By transposing A, we obtain its right kernel, which is equivalent to its left kernel.