随笔分类 -  Linear Algebra

《Introduction to Linear Algebra》by Gilbert Strang.
10. Conclusion
摘要：10.1 Matrix Factorizations A = LU = (Lower triangular L with 1's on the diagonal)(Upper triangular U with pivots on the diagonal) requirements : No ro 阅读全文
posted @ 2022-04-05 19:25 溪奇的数据 阅读(193) 评论(0) 推荐(0)
9. Complex Vectors and Matrices
摘要：9.1 Real versus Complex R= line of all real numbers (\(-\infty < x < \infty\)) \(\longleftrightarrow\) C=plane of all complex numbers \(z=x+iy\) |x| = 阅读全文
posted @ 2022-04-05 18:54 溪奇的数据 阅读(99) 评论(0) 推荐(0)
8. Linear Transformations
摘要：8.1 Linear Requires Keys: A linear transformation T takes vectors v to vectors T(v). Linearity requires: \[ T(cv +dw) = cT(v) + dT(w) \] The input vec 阅读全文
posted @ 2022-04-05 18:34 溪奇的数据 阅读(102) 评论(0) 推荐(0)
7. The Singular Value Decomposition(SVD)
摘要：7.1 Singular values and Singular vectors The SVD separates any matrix into simple pieces. A is any m by n matrix, square or rectangular, Its rank is r 阅读全文
posted @ 2022-04-05 18:16 溪奇的数据 阅读(182) 评论(0) 推荐(0)
6. Eigenvalues and Eigenvectors
摘要：Keys: What are Eigenvalues and Eigenvectors? How to find Eigenvalues and Eigenvectors? Applications of Egenvalues and Eigenvectors: Difference equatio 阅读全文
posted @ 2022-04-05 17:51 溪奇的数据 阅读(127) 评论(0) 推荐(0)
5. Determinant
摘要：5.1 The Properties of Determinants The determinant of the n by n identity matrix is 1 : \(det I = 1\). The determinant changes sign when two rows are 阅读全文
posted @ 2022-04-05 16:56 溪奇的数据 阅读(188) 评论(0) 推荐(0)
4. Orthogonality
摘要：4.1 Orthogonal Vectors and Suspaces Orthogonal vectors have \(v^Tw=0\)，and \(||v||^2 + ||w||^2 = ||v+w||^2 = ||v-w||^2\). Subspaces \(V\) and \(W\) ar 阅读全文
posted @ 2022-04-05 10:51 溪奇的数据 阅读(156) 评论(0) 推荐(0)
3. Vector Spaces and Subspaces
摘要：3.1 Vector Spaces The space \(R^n\) consists of all colunm vectors \(v\) with n components. We can add any vectors in \(R^n\) , and we can multiply an 阅读全文
posted @ 2022-04-04 12:00 溪奇的数据 阅读(206) 评论(0) 推荐(0)
2. Solving Linear Equations
摘要：2.1 Linear Equations Picture Row Picture 2 by 2 equations Two equations, Two unknowns \[ \begin{matrix} x - 2y = 1 \\ 3x + 2y = 11 \end{matrix} \] The 阅读全文
posted @ 2022-04-04 10:48 溪奇的数据 阅读(102) 评论(0) 推荐(0)
1. Vectors and Linear Combinations
摘要：1.1 Vectors We have n separate numbers \(v_1、v_2、v_3,...,v_n\)，that produces a n-dimensional vector \(v\)，and \(v\) is represented by an arrow. \[ v=\ 阅读全文
posted @ 2022-04-04 09:37 溪奇的数据 阅读(150) 评论(0) 推荐(0)