Course

Linear algebra

From systems of equations and matrices to vector spaces, linear transformations, eigenvalues and orthogonality: the shared language of data science, physics and engineering.

31concepts

6topics

310exercises

≈ 16 hof study approx.

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Course path

1
Systems and matrices 6 concepts
System of linear equations · Matrix · Matrix multiplication · Gaussian elimination · Inverse matrix · Transpose matrix
2
Determinants 4 concepts
Determinant · Cofactor and Laplace expansion · Properties of the determinant · Cramer's rule
3
Vector spaces 7 concepts
Vector in ℝⁿ · Vector space · Vector subspace · Linear combination and span · Linear independence · Basis and dimension · Rank of a matrix
4
Linear transformations 5 concepts
Linear transformation · Matrix of a linear transformation · Kernel and image · Rank–nullity theorem · Change of basis
5
Eigenvalues and eigenvectors 4 concepts
Eigenvalue and eigenvector · Characteristic polynomial · Eigenspace · Diagonalization
6
Orthogonality 5 concepts
Dot product · Vector norm · Orthogonal vectors · Orthogonal projection · Gram–Schmidt process

Sources

Gilbert Strang, Introduction to Linear Algebra, 6th edition, Wellesley-Cambridge Press, 2023.
Sheldon Axler, Linear Algebra Done Right, 4th edition, Springer, 2024.
David C. Lay, Steven R. Lay, Judi J. McDonald, Linear Algebra and Its Applications, 6th edition, Pearson, 2021.
Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence, Linear Algebra, 4th edition, Pearson / Prentice Hall, 2003.