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- https://math.libretexts.org/Bookshelves/Linear_Algebra/Matrix_Algebra_with_Computational_Applications_(Colbry)/31%3A_16_Pre-Class_Assignment_-_Linear_Dynamical_Systems/31.0%3A_IntroductionReadings for this topic (Recommended in bold) Boyd Chapter 9 pg 163-173 Goals for today’s pre-class assignment Linear Dynamical Systems Markov Models Ordinary Differential Equations Assignment wrap up
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Matrix_Algebra_with_Computational_Applications_(Colbry)/17%3A_09_Pre-Class_Assignment_-_Determinants
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Matrix_Algebra_with_Computational_Applications_(Colbry)/35%3A_18_Pre-Class_Assignment_-_Inner_Product/35.0%3A_IntroductionGoals for today’s pre-class assignment Inner Products Inner Product on Functions Assignment wrap-up
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Matrix_Algebra_with_Computational_Applications_(Colbry)/37%3A_19_Pre-Class_Assignment_-_Least_Squares_Fit_(Regression)/37.2%3A_Linear_RegressionWatch the video for using Least Squares to do linear regression. from IPython.display import YouTubeVideo YouTubeVideo("Lx6CfgKVIuE",width=640,height=360, cc_load_policy=True) Question 3 How to tell i...Watch the video for using Least Squares to do linear regression. from IPython.display import YouTubeVideo YouTubeVideo("Lx6CfgKVIuE",width=640,height=360, cc_load_policy=True) Question 3 How to tell it is a good fit or a bad one?
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Matrix_Algebra_with_Computational_Applications_(Colbry)/26%3A_13_In-Class_Assignment_-_Projections/26.2%3A_Understanding_Projections_With_Codeif len(m1[0]) != d: print("ERROR - inner dimentions not equal") result = [[0 for i in range(n)] for j in range(m)] for i in range(0,n): for j in range(0,m): for k in range(0,d): result[i][j] = result[...if len(m1[0]) != d: print("ERROR - inner dimentions not equal") result = [[0 for i in range(n)] for j in range(m)] for i in range(0,n): for j in range(0,m): for k in range(0,d): result[i][j] = result[i][j] + m1[i][k] * m2[k][j] return result a black line from the origin to “\(b\)”, a black line from origin to “\(a\)”; a green line showing the “\(a\)” component in the “\(b\)” direction and a red line showing the “\(a\)” component orthogonal to the green line.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Matrix_Algebra_with_Computational_Applications_(Colbry)/07%3A_04_Pre-Class_Assignment_-_Python_Linear_Algebra_Packages/7.0%3A_IntroductionRecommended further readings for this pre-class assignment. Beezer - Section RREF pg 22-44 Heffron - Chapter 1.I, pg 2-13 Assignment Overview The Syntax for Systems of Linear Equations Introduction to...Recommended further readings for this pre-class assignment. Beezer - Section RREF pg 22-44 Heffron - Chapter 1.I, pg 2-13 Assignment Overview The Syntax for Systems of Linear Equations Introduction to Gauss Jordan Elimination Gauss Jordan Elimination and the Row Echelon Form Gauss Jordan Practice Assignment wrap up
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Matrix_Algebra_with_Computational_Applications_(Colbry)/05%3A_03_Pre-Class_Assignment_-_Linear_Equations/5.5%3A_Assignment_wrap-upWhat questions do you have, if any, about any of the topics discussed in this assignment after working through the jupyter notebook? How well do you feel this assignment helped you to achieve a better...What questions do you have, if any, about any of the topics discussed in this assignment after working through the jupyter notebook? How well do you feel this assignment helped you to achieve a better understanding of the above mentioned topic(s)? What was the most challenging part of this assignment for you? What kind of additional questions or support, if any, do you feel you need to have a better understanding of the content in this assignment?
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Matrix_Algebra_with_Computational_Applications_(Colbry)/30%3A_15_In-Class_Assignment_-_Diagonalization/30.1%3A_Pre-class_Assignment_Review15 Pre-Class Assignment: Diagonalization and Powers
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Matrix_Algebra_with_Computational_Applications_(Colbry)/11%3A_06_Pre-Class_Assignment_-_Matrix_Mechanics/11.4%3A_Elementary_MatricesIf you multiply your matrix from the left using the elementary matrix, you will get the desired operation. Give a \(3 \times 3\) elementary matrix named E2 that swaps row 3 with row 1 and apply it to ...If you multiply your matrix from the left using the elementary matrix, you will get the desired operation. Give a \(3 \times 3\) elementary matrix named E2 that swaps row 3 with row 1 and apply it to the \(A\) Matrix. Give a \(3 \times 3\) elementary matrix named E3 that multiplies the first row by \(c=3\) and adds it to the third row. Give a \(3 \times 3\) elementary matrix named E4 that multiplies the second row by a constant \(c=1/2\) applies this to matrix \(A\).
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Matrix_Algebra_with_Computational_Applications_(Colbry)/21%3A_11_Pre-Class_Assignment_-_Vector_Spaces/21.4%3A_Assignment_wrap-upWhat questions do you have, if any, about any of the topics discussed in this assignment after working through the jupyter notebook? How well do you feel this assignment helped you to achieve a better...What questions do you have, if any, about any of the topics discussed in this assignment after working through the jupyter notebook? How well do you feel this assignment helped you to achieve a better understanding of the above mentioned topic(s)? What was the most challenging part of this assignment for you? What kind of additional questions or support, if any, do you feel you need to have a better understanding of the content in this assignment?
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Matrix_Algebra_with_Computational_Applications_(Colbry)/38%3A_19_In-Class_Assignment_-_Least_Squares_Fit_(LSF)/38.3%3A_PseudoinverseBecause the rowspace of \(A\) and the column space \(A\) have the same dimension then \(A\) is a the one-to-one mapping from the row space to the columnspace. Let's apply SVD on \(A\): \(A= U\Sigma V^...Because the rowspace of \(A\) and the column space \(A\) have the same dimension then \(A\) is a the one-to-one mapping from the row space to the columnspace. Let's apply SVD on \(A\): \(A= U\Sigma V^\top\), where \(U\) is a \(m \times m\) matrix, \(V^{\top}\) is a \(n \times n\) matrix, and \(\Sigma\) is a diagonal \(m \times n\) matrix.
