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Linear Algebra

Linear Algebra: systems of linear equations, matrices, determinants, vector spaces, linear transformations, eigenvalues, inner products, and applications.

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Linear models and systems of linear equationsStart module 1 Starting Check for this course (6 questions)

Grade University

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Up nextModule 1 · Linear SystemsLinear models and systems of linear equations
Not startedModule 2 · Linear SystemsGaussian and Gauss–Jordan elimination
Not startedModule 3 · Linear SystemsHomogeneous systems and parametric solutions
Not startedModule 4 · MatricesMatrix operations and matrix algebra
Not startedModule 5 · MatricesInverses and elementary matrices
Not startedModule 6 · MatricesBlock matrices and LU factorization
Not startedModule 7 · DeterminantsDeterminants and cofactor expansion
Not startedModule 8 · DeterminantsProperties of determinants and Cramer's rule
Not startedModule 9 · Euclidean Vector SpacesVectors, norm, distance, and the dot product
Not startedModule 10 · Euclidean Vector SpacesLines, planes, and the cross product
Not startedModule 11 · Vector SpacesVector space axioms and subspaces
Not startedModule 12 · Vector SpacesSpan and linear independence
Not startedModule 13 · Vector SpacesBasis and dimension
Not startedModule 14 · Vector SpacesRow space, column space, and null space
Not startedModule 15 · Vector SpacesRank, nullity, and the dimension theorem
Not startedModule 16 · Linear TransformationsLinear transformations, kernel, and range
Not startedModule 17 · Linear TransformationsMatrix representations of linear transformations
Not startedModule 18 · Linear TransformationsChange of basis and similarity
Not startedModule 19 · EigenvaluesEigenvalues and eigenvectors
Not startedModule 20 · EigenvaluesDiagonalization
Not startedModule 21 · EigenvaluesComplex eigenvalues
Not startedModule 22 · Inner Product SpacesInner products and orthogonality
Not startedModule 23 · Inner Product SpacesGram–Schmidt and orthonormal bases
Not startedModule 24 · Inner Product SpacesOrthogonal projections and least squares
Not startedModule 25 · Inner Product SpacesSymmetric matrices and orthogonal diagonalization
Not startedModule 26 · ApplicationsQuadratic forms
Not startedModule 27 · ApplicationsMarkov chains
Not startedModule 28 · ApplicationsSystems of linear differential equations
Not startedModule 29 · Numerical MethodsError and stability in linear computations