摘要:
Four fundamental subspaces( for matrix A) if A is m by n matrix: Column space C(A) in Rm (列空间在m维实空间中) Null space N(A) in Rn Row space C(A^)(^代表转置)in R 阅读全文
摘要:
Linear independence Spanning a space Basis and dimension 以上概念都是针对a bunch of vectors, 不是矩阵里的概念 Suppose A is m by n with m<n, then there are non-zero so 阅读全文
摘要:
Compute solution of AX=b (X=Xp+Xn) rank r r=m solutions exist r=n solutions unique example: 若想方程有解,b1,b2,b3需要满足什么条件? 观察矩阵可知,第三行是前两行的和,所以b1+b2=b3 Solva 阅读全文
摘要:
Computing the nullspace (Ax=0) Pivot variables-free variables Special solutions: rref( A)=R rank of A=the number of pivots=2 由上述矩阵行变换回代可得方程 我们自行给free 阅读全文
摘要:
Vector spaces and subspaces Column space of A solving Ax=b Null space of A Vector space requirements v+w and cv are in the space All combs cv+dw are i 阅读全文
摘要:
Section 2.7 PA=LU and Section 3.1 Vector Spaces and Subspaces Transpose(转置) example: 特殊情况,对称矩阵(symmetric matrices),例如: 思考:R^R(R的转置乘以R)有什么特殊的? 回答:alway 阅读全文
摘要:
Inverse of AB,A^(A的转置) Product of elimination matrices A=LU (no row exchanges) Inverse of AB,A^(A的转置): Product of elimination matrices A=LU (no row ex 阅读全文
摘要:
Matrix multiplication(4 ways!) Inverse of A Gauss-Jordan / find inverse of A Matrix multiplication 1、点积法 2、matrix * column=comb of columns columns of 阅读全文
摘要:
Lecture2 Elimination Inverses Permutation 消元法介绍(elimination): 有方程组 提取系数,形成矩阵为: 消元的思想跟解方程组中先消除未知数的思路一致,通过数乘(multiply)和减法(substract)化简,化简过程为: 以上红框起来的数字叫 阅读全文
摘要:
Professor: Gilbert Strang Text: Introduction to Linear Algebra http://web.mit.edu/18.06 Lecture 1 contents: n linear equation, n unknowns Row picture 阅读全文