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calculating the sum of the diagonals of a matrix is an important task in many mathematical and data applications. in this tutorial, we'll explore how to compute the sums of both the primary (main) diagonal and the secondary (anti-diagonal) of a square matrix using python.

understanding the diagonals of a matrix

1. **primary diagonal**: this runs from the top-left to the bottom-right of the matrix. for a matrix `a`, the elements of the primary diagonal are `a[i][i]` where `i` is the index.

2. **secondary diagonal**: this runs from the top-right to the bottom-left of the matrix. the elements of the secondary diagonal in a matrix `a` are `a[i][n-1-i]` where `n` is the size of the matrix (assuming it is square).

steps to calculate the sum of diagonals

1. create a square matrix (2d list).
2. initialize variables to store the sums of the primary and secondary diagonals.
3. loop through the indices of the matrix to add up the elements of both diagonals.
4. print the results.

code example

here's a python code example that demonstrates how to calculate the sums of the diagonals of a square matrix.



explanation of the code

1. **function definition**: the function `calculate_diagonal_sums(matrix)` takes a square matrix as an input.

2. **initialization**: it initializes `primary_diagonal_sum` and `secondary_diagonal_sum` to zero. the size of the matrix `n` is determined using `len(matrix)`.

3. **looping through the matrix**: a for-loop iterates through the indices of the matrix:
the primary diagonal elements are accessed using `matrix[i][i]`.
the secondary diagonal elements are accessed using `matrix[i][n - 1 - i]`.

4. **returning the sums**: after the loop, the function returns the sums of both diagonals.

5. **example usage**: the example matrix is defined, and the function is called. the results are printed.

conclusion

this tutorial covered how to calculate the sums of the primary and secondary diagonals of a square matrix in python. the app ...

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