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Linear algebra18

Linear Algebra for Machine Learning and Data Science (17) Determinants and EigenvectorsCheck your knowledgeQ1If

$\text{det } M = 20$ and

$\text{det } N = 10$ , and

$M, N$ have the same size. What is the value of

$\text{det } M\cdot N$ and

$\text{det}(N^{-1})$ ? (Videos: Determinant of a product, Determinant of inverses)Answer더보기

$\det M\cdot N$ is 200 and

$\det(N^{-1})$ is 1/10 or 0.1Q2Does the set

$\{(1,2),(4,8)\}$ form a base for

$\mathbb{R}^2$ ? (Videos.. 2024. 8. 20.

Linear Algebra for Machine Learning and Data Science (16) Determinants and EigenvectorsEigenvalues and EigenvectorsDimensionality Reduction and ProjectionDimensionality reduction helps preserve information and helps with visualization in exploratory analysis.Without it, we would be removing features that lead to losing information.Projection: Moving data points into a vector space in different dimensionsHere we are talking about dimensionality reductio.. 2024. 8. 19.

Linear Algebra for Machine Learning and Data Science (15) Determinants and EigenvectorsEigenvalues and EigenvectorsBases in Linear AlgebraA matrix can be seen as a linear transformation from a plane to a planeBasis: Two vectors coming from the origin that define the plots (square, parallelogram, etc)The main property of basis is that every point in the space can be expressed as a linear combination of elements in the basesTwo vectors that go in the sam.. 2024. 6. 7.

Linear Algebra for Machine Learning and Data Science (14) Determinants and EigenvectorsQuizQ1Let

$T$ be a linear transformation in the plane represented by the following matrix:

$\left[\begin{array}{cc}1&0\\2&3\end{array}\right]$ The rank of

$T$ is:1032Answer더보기4At this point of the course, you have several ways of finding this information. Applying what you've seen in the lecture on Singularity and rank of linear transformations, it is necessary to .. 2024. 6. 5.

Linear Algebra for Machine Learning and Data Science (13) Determinants and EigenvectorsIn this final week, you will take a deeper look at determinants. You will learn how determinants can be geometrically interpreted as an area and how to calculate determinants of product and inverse of matrices. We conclude this course with eigenvalues and eigenvectors. Eigenvectors are used in dimensionality reduction in machine learning. You will see how eigenvector.. 2024. 6. 4.

Linear Algebra for Machine Learning and Data Science (12) Vectors and Linear TransformationsCheck your knowledgeQ1If

$\vec u=(3,6)$ and

$\vec v=(5,2)$ , compute

$\vec{u}+\vec{v}$ and

$\vec{u}-\vec{v}$ . (Videos: Vectors and their properties, Sum and difference of vectors)더보기Addition: (8, 8)Subtraction: (-2, 4)Q2What is the distance between vectors

$\vec u$ and

$\vec v$ ? (Video: Distance between vectors)더보기L1-distance: 6L2-distance:

$\sqrt{20}$ Q3If $\vec .. 2024. 5. 17.

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