Matrix theory is a fundamental mathematical framework that underpins the principles of quantum computation, facilitating the manipulation and analysis of quantum systems. In quantum mechanics, information is represented using quantum bits, or qubits, which can exist in superpositions of states. Matrix theory provides the tools necessary to describe these qubit states as vectors in complex vector spaces, allowing for the efficient representation of multi-qubit systems through tensor products. Quantum gates, the basic building blocks of quantum circuits, are represented by unitary matrices, ensuring the preservation of probability amplitudes during operations. The application of matrix operations is crucial in the formulation of quantum algorithms, such as Grover's search and Shor's factoring algorithm, which leverage the unique properties of quantum mechanics to achieve computational advantages over classical algorithms.