A novel concept of composite-lattice-based liquid crystalline phases is presented in this article. The author explains and proves this concept from linear algebra and X-ray crystallography. When the ab faces in a 3D crystal continuously rotate and/or slip between each other by heating, the 3D vector space is disintegrated at the first step into the 2D subspace and the 1D subspace. This state can be described as [2D circle plus 1D] composite vector subspaces in linear algebra. [2D circle plus 1D] is not equal to 3D and the mathematical sign circle plus means direct sum in linear algebra. The [2D circle plus 1D] liquid crystalline phase is composite-lattice-based. Besides the [2D circle plus 1D] phase, two other composite-lattice-based liquid crystalline phases having [1D circle plus 1D] and [1D circle plus 1D circle plus 1D] can be also theoretically considered from linear algebra. In this article, these real-life examples are also demonstrated at the first time.