On the Role and Importance of Direct Sum Decomposition Thinking Way of Linear Space

The theory of linear space is the main content of advanced algebra, and also the core of advanced algebra; the direct sum decomposition thinking is a powerful tool in studying the linear space structure. The role of the direct sum decomposition thinking in mathematics, algebra and in students’ learning process was expounded. Also discussed in the paper is the crucial role the direct sum decomposition thinking plays in learning of this course and other successive courses and in cultivating students’ thinking ability.