This paper continues the study of associative and Lie deep matrix algebras, ${\mathcal{DM}}(X,{\mathbb{K}})$ and ${\mathfrak{gld}}(X,{\mathbb{K}})$ , and their subalgebras. After a brief overview of the general construction, balanced deep matrix subalgebras, ${\mathcal{BDM}}(X,{\mathbb{K}})$ and ${\mathfrak{bld}}(X,{\mathbb{K}})$ , are defined and studied for an infinite set X. The global structures of these two algebras are studied, devising a depth grading on both as well as determining their ideal lattices. In particular, ${\mathfrak{bld}}(X,{\mathbb{K}})$ is shown to be semisimple. The Lie algebra ${\mathfrak{bld}}(X,{\mathbb{K}})$ possesses a deep Cartan decomposition and is locally finite with every finite subalgebra naturally enveloped by a semi-direct product of ’s. We classify all associative bilinear forms on (a natural depth analogue of ) and .