Vektorit ja matriisit, 5 cr
- Description
- Completion options
- Completion option 1
- Completion option 2
- Completion option 3
- Completion option 4
- Completion option 5
Vektorit ja matriisit (Participation in teaching in English), englanti
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.