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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
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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
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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
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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
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Keys: What are Eigenvalues and Eigenvectors? How to find Eigenvalues and Eigenvectors? Applications of Egenvalues and Eigenvectors: Difference equatio 阅读全文
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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
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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