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I have a big matrix and I have partitioned it. So, I want to say that I am taking the summation of entries that do not belong to the blocks in the diagonal. How can I say it mathematically.

Is it correct to define:

$A = \{(i, j): (i,j) \in \Omega_{kl}, \forall k \neq l; i, j= 1, 2,...p; k, l=1, 2,..., M\}$

M is the total number of blocks. p is the dimension of big matrix which I have partitioned.

Any help is greatly appreciated.

shani
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1 Answers1

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I would say something like...

Let $A$ partitioned in blocks as $A = \lbrack B_{i,j} \rbrack$, and let $S = \Sigma_{i \neq j} (\mathbf r_{i} B_{i,j} \mathbf c_{j})$ where $\mathbf r_i$, and $\mathbf c_j$ are the corresponding row and column all 1's vectors according to the dimensions of $B_{i,j}$

Assuming the partition is somehow homogeneous, etc. (Entry sum inspired here)

Hope helps.

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carlosayam
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