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Let $\\mathcal{V}$ denote an $(h+k)$-dimensional vector space over $\\mathbb{F}_{q}$. Let the set $P$ consist of the subspaces of $\\mathcal{V}$. The set $P$, together with the inclusion partial order, is a poset called a projective geometry. We define a matrix $A\\in \\text{Mat}_{P}(\\mathbb{C})$ as follows. 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A projective geometry is defined as follows. Let $h>k\\geq 1$ denote integers. Let $\\mathbb{F}_{q}$ denote a finite field with $q$ elements. Let $\\mathcal{V}$ denote an $(h+k)$-dimensional vector space over $\\mathbb{F}_{q}$. Let the set $P$ consist of the subspaces of $\\mathcal{V}$. The set $P$, together with the inclusion partial order, is a poset called a projective geometry. We define a matrix $A\\in \\text{Mat}_{P}(\\mathbb{C})$ as follows. 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