We assume that this statement is false, but one of the most common mathematical errors.
So a question arises: what is the importance of the LHS diagonal?
P( n by n) be the matrix of ones along the reverse diagonal and zero elsewhere , this is a permutation matrix, hence det(P) = +1 or -1, det() stands for the matrix determinant.
It can be observed that P(n by n) *P(n by n) = Identity (n by n) regardless of n is even or odd.
therefore: det(A - lamda*P) = (+1 or -1) *det( A*P - lambda*Identity(n by n)), for any square matrix A ( n by n).
https://math.stackexchange.com/questions/227345/name-for-diagonals-of-a-matrix
Important or not? As a question it is too general, no definite answer could be given. It depends.
Here is what we find on Google research concerning the main diagonal
,
[Central Connecticut State University
https://chortle.ccsu.edu › vmch13 › vmch13_17
main diagonal
If the matrix is A, then its main diagonal are the elements whose row number and column number are equal, ajj.]
{{The other diagonal of a matrix does not matter and has no name.}}
We assume that this statement is false, but one of the most common mathematical errors.
So a question arises: what is the importance of the LHS diagonal?
One of the important applications of the other diagonal (we call it LHS Diagonal)
[is that it can accurately derive the well-known normal/Gaussian distribution law in a direct and simple way as explained in detail in references 1 and 2.]
Ref
1&2-I.M.Abbas, Do Probability and Statistics Belong to Physics or Mathematics,
Researchgate Mars 2023 and IJISRT review Mars 2023.
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