Università Roma Tre

THE BLACKBOARD PLANE AS A 2-DIMENSIONAL AFFINE POINT SPACE. POINTS AND VECTORS: DIFFERENCE BETWEEN TWO POINTS, SUM OF A POINT AND A VECTOR, SUM OF TWO VECTORS. PARALLELOGRAMS. LINEAR COMBINATION AND INTERPOLATION. DEPENDENCE AND INDEPENDENCE. AFFINE MAPS.
AFFINE SPACES OF DIMENSION 3 AND BEYOND. SAME AS ABOVE IN GENERAL DIMENSIONS. PARALLELEPIPEDS.
LINEAR SPACES. LINEAR STRUCTURE PROPERTIES. LINEAR MAPS. NULLSPACE AND RANGE. LINEAR ISOMORPHISMS AND AUTOMORPHISMS. BASES. SUBSPACES. PROJECTIONS. DIRECT SUM. LINEAR EQUATIONS. LINEAR SPACES OF LINEAR MAPS. COMPOSITION OF LINEAR MAPS. THE GENERAL LINEAR GROUP.
AREA AND VOLUME. AFFINE AREAS AND VOLUMES. DETERMINANTS OF LINEAR MAPS. THE SPECIAL LINEAR GROUP.
THE BLACKBOARD PLANE AS A 2-DIMENSIONAL EUCLIDEAN POINT SPACE. INNER PRODUCT BETWEEN TWO VECTORS. THE INDUCED NORM OF A VECTOR. ANGLE BETWEEN TWO VECTORS. DISTANCE BETWEEN TWO POINTS. EUCLIDEAN MAPS AND RIGID TRANSFORMATIONS. ORTHONORMAL BASES. THE ADJOINT OF A LINEAR MAP. SYMMETRIC AND SKEW-SYMMETRIC MAPS. ORTHOGONAL PROJECTIONS.
EUCLIDEAN SPACES OF DIMENSION 3 AND BEYOND. SAME AS ABOVE IN GENERAL DIMENSIONS. THE (3D-SPECIFIC) CROSS PRODUCT BETWEEN TWO VECTORS.
CHARACTERISTIC VECTORS AND CHARACTERISTIC VALUES. ALGEBRAIC AND GEOMETRIC MULTIPLICITY OF CHARACTERISTIC VALUES. ADAPTED BASES.
A GLIMPSE INTO NONLINEAR GEOMETRY. WHY LINEAR GEOMETRY MATTERS ALSO FOR NONLINEAR GEOMETRIC OBJECTS.

LANG, SERGE, INTRODUCTION TO LINEAR ALGEBRA (2ND EDITION), SPRINGER 2012.
ROBINSON, GILBERT DE BEAUREGARD, VECTOR GEOMETRY, DOVER 2011.
NOTES PROVIDED BY THE INSTRUCTOR.