The notion of Jacobson graph and n-array Jacobson graph of a commutative ring were introduced in 2012 and 2018, respectively, by Azimi et al and Ghayour et al. In this article we generalize them to matrix Jacobson graph. Let R be a commutative ring. The matrix Jacobson graph of a ring R, denoted J(R)m×n, is defined as a graph with vertex set is the set of matrix of ring without the matrix of its Jacobson such that two distinct vertices A; B are adjacent if and only if 1 − det(AtB) is not a unit of ring. In this article we study the matrix Jacobson graph where the underlying ring R is a finite field. Since any matrix of size m × n over a field F can be considered as a linear mapping from linear space Fm to Fn, we employ the structure of linear mappings on finite dimensional vector spaces to derive some properties of square and non square matrix Jacobson graph of fields, including their diameters.

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