Linear Algebra for Beginners: Open Doors to Great Careers 2 (Udemy)

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Learn the core topics of Linear Algebra to open doors to Computer Science, Data Science, Actuarial Science, and more! (1) Introduction Introduction Norms for Rn Distance Between Vectors in Rn Angle Between Vectors in Rn Problem Set: Norms and Dot Product for Rn Solutions to Problem Set: Norms and Dot Product for Rn Inner Product […]

Linear Algebra Tutorial: Determinants (Udemy)

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Learn everything you need to know to solve problems involving determinants (1) Introduction Introduction Matrices review Determinants of higher order: definition Determinants of higher order: practice (easy) Determinants of higher order: practice (intermediate) Cofactor expansion: theorem Cofactor expansion: practice (easy) Cofactor expansion: practice (easy) Properties of determinants: theory Properties of determinants: theory Properties of determinants: […]

Linear Algebra for Beginners: Open Doors to Great Careers (Udemy)

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Learn the core topics of Linear Algebra to open doors to Computer Science, Data Science, Actuarial Science, and more! (1) Introduction Introduction Lecture Gaussian Elimination Gaussian Elimination and Row Echelon Form Problem Set Gaussian Elimination Solutions to Problem set Gaussian elimination Detailed Solutions to Problem Set Gaussian Elimination Elementary Row Operations Elementary Row Operations: Additional […]

Alternate coordinate systems (bases) (Khan Academy)

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We explore creating and moving between various coordinate systems. (1) Orthogonal complements Orthogonal complements dim(v) + dim(orthogonal complement of v) = n Representing vectors in rn using subspace members Orthogonal complement of the orthogonal complement Orthogonal complement of the nullspace Unique rowspace solution to Ax = b Rowspace solution to Ax = b example (2) […]

Matrix transformations (Khan Academy)

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Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations. (1) Functions and linear transformations A more formal understanding of functions Vector transformations Linear transformations Visualizing linear transformations Matrix from visual representation of transformation Matrix vector products as linear transformations Linear transformations as matrix vector products Image […]

Vectors and spaces (Khan Academy)

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Let’s get our feet wet by thinking in terms of vectors and spaces. (1) Vectors Vector intro for linear algebra Real coordinate spaces Adding vectors algebraically & graphically Multiplying a vector by a scalar Vector examples Scalar multiplication Unit vector notation Unit vectors Add & subtract vectors Add vectors: magnitude & direction to component Parametric […]

Khan Academy

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Khan Academy is perhaps the best known free collection of online courses. The subjects span a great range of topics, including everything from math and science to art history. According to their about page: Our mission is to provide a free, world‑class education for anyone, anywhere. A full list of the subjects they offer is […]