Transcription of Linear Algebra in Twenty Five Lectures
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Linear Algebra in Twenty Five Lectures
Linear Algebra in Twenty Five LecturesTom Denton and Andrew WaldronMarch 27, 2012 Edited by Katrina Glaeser, Rohit Thomas & Travis Scrimshaw1 Contents1 What is Linear Algebra ?122 Gaussian Notation for Linear Systems .. Reduced Row Echelon Form .. 213 Elementary Row Operations274 Solution Sets for Systems of Linear Non-Leading Variables .. 355 Vectors in Space, Directions and Magnitudes .. 466 Vector Spaces537 Linear Transformations588 Matrices639 Properties of Block Matrices .. The Algebra of Square Matrices.. 7310 Inverse Three Properties of the Inverse .. Finding Inverses .. Linear Systems and Inverses .. Homogeneous Systems .. Bit Matrices .. UsingLUDecomposition to Solve Linear Systems .. Finding anLUDecomposition.. BlockLDUD ecomposition .. 94212 Elementary Matrices and Permutations .. Elementary Matrices .. 10013 Elementary Matrices and Determinants II10714 Properties of the Determinant of the Inverse.
These linear algebra lecture notes are designed to be presented as twenty ve, fty minute lectures suitable for sophomores likely to use the material for applications but still requiring a solid foundation in this fundamental branch
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