Linear Algebra
Linear Algebra is the language of modern applied mathematics—and once you learn it, you’ll see it everywhere. From computer graphics to machine learning, from quantum physics to economics, linear algebra provides the tools to describe and manipulate multi-dimensional relationships. At its heart, linear algebra asks: how do things scale and add? That simple question leads to vectors, matrices, transformations, and a whole new way of seeing the mathematical world. This course takes you from the intuitive geometry of arrows in space to the powerful abstraction of vector spaces and eigenvalues.
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Vectors—Arrows in Space→
Discover the mathematical objects that have both magnitude and direction
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Vector Operations→
Learn how to add, subtract, and scale vectors
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The Dot Product→
Multiply vectors to measure alignment and compute angles
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Systems of Linear Equations→
See how linear algebra naturally arises from solving multiple equations
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Introduction to Matrices→
Meet the rectangular arrays that organize and transform data
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Matrix Multiplication→
Learn the surprising rule for multiplying matrices
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Gaussian Elimination→
Master the systematic method for solving any linear system
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Matrix Inverses→
Find the matrix that undoes what another matrix does
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Determinants→
Compute the single number that reveals whether a matrix is invertible
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Vector Spaces and Subspaces→
Abstract the idea of 'vectors' beyond arrows to any objects that add and scale
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Linear Independence and Basis→
Identify the essential building blocks of a vector space
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Linear Transformations→
Understand functions that preserve the structure of vector spaces
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Eigenvalues and Eigenvectors→
Discover the special vectors that only get scaled by a transformation
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Diagonalization→
Simplify matrices by changing to the eigenvector basis