Quantum coherence is known as an important resource in many quantum information tasks, which is a basis-dependent property of quantum states. In this paper, we discuss quantum incoherence based simultaneously on k bases using Matrix Theory Method. First, by defining a correlation function of two orthonormal bases e and f, we investigate the relationships between sets and of incoherent states with respect to e and f. We prove that if and only if the rank-one projective measurements generated by e and f are identical. We give a necessary and sufficient condition for the intersection to include a state except the maximally mixed state. Especially, if two bases e and f are mutually unbiased, then the intersection has only the maximally mixed state. Secondly, we introduce the concepts of strong incoherence and weak coherence of a quantum state with respect to a set of k bases and propose a measure for the weak coherence. In the two-qubit system, we prove that there exists a maximally coherent state with respect to when and it is not the case for .