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I have a $2\times2$ block matrix $M$ defined as follows:

$$\begin{pmatrix}X+|X| & X-|X| \\ Y-|Y| & Y+|Y|\end{pmatrix}$$

where $X$ and $Y$ are $n\times n$ matrices and $|X|$ denotes the modulus of the entire matrix $X$ that essentially comprises modulus of individual elements of $X$.

How may I find the determinant of the matrix $M$ in terms of $X$ and $Y$? Looking for a simplified solution?

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    I've only seen a solution to this kind of problem when either X+|X| or Y+|Y| are invertable. Can this be assumed in your problem?2011-12-23
  • 0
    yes assume the non singularity of the matrices.2011-12-23

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