分塊矩陣及應用
摘 要
矩陣是1種新的運算對象，我們應該充分注意矩陣運算的1些特殊規律。爲了研究問題的.需要，適當地對矩陣進行分塊，把1個大矩陣看成是由1些小矩陣塊爲元素組成的，這樣可使矩陣的結構看的更清楚。矩陣分塊的思想在線性代數證明、應用中是10分有用的。運用矩陣分塊的思想，可使解題更簡潔，思路更開闊。本文將矩陣分塊的方法到
行列式運算、解線性方程組、判斷向量線性相關性及有關矩陣秩的證明，特別是找出在2次型化標準形中的應用。
關鍵詞：分塊矩陣；線性代數；矩陣的秩；初等矩陣
Block Matrix and Its Application
Abstract
Matrix is a kind of new operation target, and we should pay full attention to the special law in operating the matrix. In order to make the structure of matrix more clearly, when we study this matter, we can divide matrix properly, and regard a big matrix as some small ones, which integrate it. The thought of dividing matrix into blocks is very important in proving and applying the linear algebra. Use the thought of dividing matrix to blocks can help us to solve problems more pithily and think methods more widely. This thesis uses the blocking matrix method into the calculation of determinant, tries to solve the linear equations, Vector judgment linear correlation matrix and the proof of other relative Matrix rank , especially in finding the applications in the secondary-type standards.
Key words: Block matrix；linear algebra；rank of matrix；elementary matrix