1

I have a matrix, say $A$ and want to find it's determinant $detA$. A is $L\times L$ and made up of $2\times 2$ blocks $M_{i,j}$ giving it a total size of $2L \times 2L$.

The entries of the blocks $M_{i,j}$ depend on $i$ and $j$ but apart from that they are the same.

Is there an easy way to calculate the determinant? Does the symmetry help in any way?

user213529
  • 31
  • If $M_{i,j}=0$ for $i>j$, then $|A|=|M_{1,1}||M_{2,2}|\cdots |M_{L,L}|$. (block upper triangular) – vadim123 Mar 02 '15 at 19:25
  • Have you tried to look at wiki? – iiivooo Mar 02 '15 at 19:27
  • Sorry, that's not what I meant. Really what I wanted to say that each $M_{ij}$ is a $2 \times 2$ matrix and the entries of the blocks are functions of $i$ and $j$. Can the determinant be decomposed into some product or sum of the determinants of the blocks? @markfischler – user213529 Mar 02 '15 at 20:59

1 Answers1

1

I think you are saying that all the $2\times 2$ blocks are identical to each other.

(I can think of no other meaning to the phrase "they are the same".)

In that case, the determinant of the matrix is zero, since the first and third rows are identical, hence linearly dependent.

Mark Fischler
  • 41,743