• Diagonalization of symmetric matrices by congruence. (13'49'')

• Interpretation of the orientation of a basis. (4'59'')
• Construcction of a rotation matrix in $R^3$. (6'14'')
• Construction of symmetries in $R^3$. (5'25'')
• Classificaction of othogonal maps in  $R^3$. (14'38'')

Chapter 4. Cross product and mixed product.

• Cross product and mixed product (6'39'')

• Definition of affine space. (3'56'')
• Affine references. (8'03'')
• Affine subvarieties. (2'20'')
• Equations of a line it the plane. (6'22'')
• Equations of lines and planes in the space. (9'45'')
• Distance between affine varieties. (5'09'')
• Distance from a point to a line in the plane. (6'21'')
• Distance from a point and a line and a plane in the space. (12'34'')
• Distance between two skew lines. (10'35'')
• Affine transformations. (3'16')
• Traslations. (1'55'')
• Homotethies. (4'45'')
• Isometries. (6'48'')
• Pencils of lines and planes. (8'03'')

• Introduction to conics. (10'38'')
• Polar line and tangente linea at a point respect to a conic. (8'45'')
• Center of a conic. (5'28'')
• Asymptote and astmptotic directions of a conic. (8'37'')
• Axes and vertices of a conic. (7'43'')
• Focus, directrix lines and eccentricity of a conic. (3'02'')
• Canonical form of the ellipse. (5'45'')
• Canonical form of the hyperbola. (4'29'')
• Canonical form of the parabole. (3'03'')
• Introduction to pencil of conics. Pencil of conics for 4 potins. (4'40'')
• Pencil of conics throigh three points and the tangent in one of them. (4'20'')
• Pencil of conics for two points and the tangent in one of them, (5'52'')