Mathematics · Avançado · Nível 1

Linear algebra

Linear equations and the augmented matrix; Gaussian elimination, the reduced row echelon form and the solution set; rank, consistency and homogeneous systems; matrix arithmetic, multiplication as composition, inverses by row reduction and the LU factorisation; determinants by cofactor expansion and by row operations, with Cramer's rule and the reading of a determinant as an area; vector spaces and subspaces, span, independence, bases, dimension, the four fundamental subspaces and the rank-nullity theorem; linear maps and their matrices, kernel and image, coordinates and change of basis; the characteristic polynomial, eigenvectors, diagonalisation and matrix powers; the dot product, projections, Gram-Schmidt and least squares; and the spectral theorem with an introduction to the singular value decomposition.

Ages 18+ 30 lessons about 13.5 hours in all

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