Linear algebra Last updated Mar 3, 2020 Page ID21840 Save as PDF NumberOfHamiltonian.pg Abstract vector spaces Abstract vector spacesBasis and dimensionCoordinate vectors and change of basisDefinition and propertiesExamplesLinear combinationsLinear independenceSpanSubspacesShow allDeterminantsApplicationsComputing determinantsPropertiesEigenvalues and eigenvectorsApplicationsComplex eigenvalues and eigenvectorsComputing eigenvalues and eigenvectorsPropertiesQuadratic formsEuclidean spacesBasis and dimensionCoordinate vectors and change of basisLinear combinationsLinear independenceRow, column, and null spacesSpanSubspacesVectorsShow allInner productsApplicationsComputing with dot productsComputing with inner productsGram-Schmidt processOrthogonal and orthonormal setsOrthogonal matricesProjection and distanceShow allLinear transformationsAssociated matricesEvaluating linear transformationsInversesKernel and imageOne-to-one and ontoPropertiesMatricesComplex entriesEchelon formElementary matricesInversesMarkov chainsMatrix algebraRankRow operationsTranspose and traceShow allMatrix factorizationsDiagonalizationJordan formLU factorizationQR factorizationSingular value decompositionSystems of linear equationsApplicationsAugmented matricesMatrix-vector formsSystems with 2 variablesSystems with 3 variablesSystems with 4 or more variablesVector equationsShow allVector geometryCoordinate systemsCross productDot product, length, and unit vectorsLinesLines with planesPlanesVectors and vector arithmeticShow all