Introduction to Linear Algebra and to Mathematics for Machine Learning-Welcome to this course
Introduction: Solving data science challenges with mathematics
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About Imperial College & the team
How to be successful in this course
Grading policy
Additional readings & helpful references
Introduction to Linear Algebra and to Mathematics for Machine Learning-The relationship between machine learning, linear algebra, and vectors and matrices
Motivations for linear algebra
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Getting a handle on vectors
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Introduction to Linear Algebra and to Mathematics for Machine Learning-Vectors
Operations with vectors
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Introduction to Linear Algebra and to Mathematics for Machine Learning-Summary
Summary
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Vectors are objects that move around space-Introduction
Introduction to module 2 - Vectors
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Vectors are objects that move around space-Finding the size of a vector, its angle, and projection
Modulus & inner product
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Cosine & dot product
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Projection
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Vectors are objects that move around space-Changing the reference frame
Changing basis
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Basis, vector space, and linear independence
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Applications of changing basis
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Vectors are objects that move around space-Doing some real-world vectors examples
Summary
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Matrices in Linear Algebra: Objects that operate on Vectors-Introduction to matrices
Matrices, vectors, and solving simultaneous equation problems
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Matrices in Linear Algebra: Objects that operate on Vectors-Matrices in linear algebra: operating on vectors
How matrices transform space
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Types of matrix transformation
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Composition or combination of matrix transformations
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Matrices in Linear Algebra: Objects that operate on Vectors-Matrix Inverses
Solving the apples and bananas problem: Gaussian elimination
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Going from Gaussian elimination to finding the inverse matrix
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Matrices in Linear Algebra: Objects that operate on Vectors-Special matrices and Coding up some matrix operations
Determinants and inverses
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Summary
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Matrices make linear mappings-Matrices as objects that map one vector onto another; all the types of matrices
Introduction: Einstein summation convention and the symmetry of the dot product
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Matrices make linear mappings-Matrices transform into the new basis vector set
Matrices changing basis
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Doing a transformation in a changed basis
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Matrices make linear mappings-Making Multiple Mappings, deciding if these are reversible
Orthogonal matrices
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Matrices make linear mappings-Recognising mapping matrices and applying these to data
The Gram–Schmidt process
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Example: Reflecting in a plane
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Eigenvalues and Eigenvectors: Application to Data Problems-What are eigen-things?
Welcome to module 5
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What are eigenvalues and eigenvectors?
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Eigenvalues and Eigenvectors: Application to Data Problems-Getting into the detail of eigenproblems
Special eigen-cases
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Calculating eigenvectors
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Eigenvalues and Eigenvectors: Application to Data Problems-When changing to the eigenbasis is really useful
Changing to the eigenbasis
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Eigenbasis example
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Eigenvalues and Eigenvectors: Application to Data Problems-Making the PageRank algorithm
Introduction to PageRank
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Eigenvalues and Eigenvectors: Application to Data Problems-Eigenvalues and Eigenvectors: Assessment
Summary
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Wrap up of this linear algebra course
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