How to calculate the determinant of a symbolic matrix 5x5

Suppose we have a symmetric,real matrix,K 5x5: K = [0 0 0 F 0; 0 0 F E 0;0 F E D 0;F E D C 0;0 0 0 0 A]

A,C,D,E,F are matrices (their size does not matter to me). How can i say to matlab to consider these entries as matrices and thereafter calculating the determinant of K ?

[Walter Roberson]

Are A, C, D, E, F each square matrices? Are they the same size as each other? And should the zeroes be implicitly expanded to match the size of the matrices?

e.g., if each matrix is nxn and Z represents zeros(n,n) then you have K = [Z Z Z F Z; Z Z F E Z] and so on?

Answer 1

[Ahmed A. Selman]

I don't think it is possible to concatenate a matrix such as K if A-F have sizes > (1,1), thus no value of the determinant exist. This is because if e.g., [E] exists, then K(1,:)=[0 0 0 F 0] and K(2,:)=[0 0 F E 0] must be the same size, hence (E = [E], e.f., E is 1 by 1 matrix).

If the matrix K do exist, please explain further what is the shape of A-F sub matrices.

Otherwise just use the regular concatenation functions (cat, vertcat or horzcat) to construct K from A-F submatrices, and det(K) to find the determinant.

[Salvo]

Thank you very much Ahmed, you answered to my question. The entries are matrices of real numbers and this particular matrix's layout is for solving an eingeproblem. I have tried also with mathematica by wolfram,that's great but i can't verify whether is correct or not because that software arranges the matrix multiplication on the base of the alphabetic order, and this doesn't keep into account the noncommutative property of the addition for the matrices. So i can't establish whether is right or wrong,it means i have to proceed by hand which is quite annoying..

[Walter Roberson]

looks like it might be det(F)^4*det(A) with no component of C, D, or E.