Vektorit ja matriisit, Lectures in English

Vectors: geometry and algebra of vectors; length, angle, dot product, projections; lines and planes.

Linear equations: augmented matrix, Gaussian and Gauss-Jordan elimination, spanning sets and linear independence, applications.

Matrix addition, scalar multiplication, multiplication, block multiplication, power, transpose.

Inverse and rank of matrices: inverse properties, elementary matrices, Gauss-Jordan method for inverse; subspace, column space, row space, null space, basis, dimension, rank, nullity, conditions for invertibility, coordinates with respect to a basis.

Determinant of a matrix: cofactor expansion formula, determinant properties, matrix invertibility; Leslie population model; cross product and scalar triple product.

Eigenvalues and eigenvectors, algebraic multiplicity, geometric multiplicity; similar matrices, diagonalisation, powers of a diagonalisable matrix.