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What is Linear Algebra?

Linear Algebra is the study of linear maps between vector spaces and the matrix algebra necessary to apply the theory to concrete problems. Its roots are quite modest: solving systems of linear equations. Linear algebra, however, has developed substantially and permeates most of modern mathematics and much of modern science and engineering. In this class, we will cover many topics of linear algebra, including Gaussian elimination, matrix algebra, $LU$ factorization, vector spaces, subspaces, dimension, norms and inner products, positive definite matrices, minimization, nearest point and least squares, data fitting, orthogonality, Gram-Schmidt method, the Fast Fourier Transform, and the revolutionary page rank algorithm.

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