Álgebra Lineal II. Ejemplos interactivos.

Review of Linear Algebra I.
	Example of diagonalizaction by congruence of a 3x3 matrix and transition matrix calculation. How to decide when two matrices are congruent.
PART II. Euclidean vector spaces.
	Chapter 3. Othogonal maps. Example of calculating a rotation matrix with the usual dot product, Example of calculating a rotation matrix with a NON usual dot product E xample of calculating a symmetry matrix espect to a plane with the usual dot product . Example of caculating a symmetry matrix respect to a plane with a NON usual dot product. Example of calculating a symmetry matrix respect to a line with the usual dot product. Example of classification of two orthogonal maps in the space
PART III. The affine space.
	Chapter 1. The affine space. Reference change example. Example of equations of a line in the plane knowing a point and the directiom vector. Example of equations of a line in the plane knowing a point and the normal vector Example of equations of a line in the space throught two given point s. Example of equations of a plane knowing two poins and a parallel line. Example of calculating the distance from a point to a line in the plane with the usual dot product. Example of calculating the distance from a point to a line in the plane with a NON usual dot prodcut. Example of calculating of the distance from a point to a line in the space with the usual dot product. Example of calculating the distance from a point to a line in the space wirh a NON usal dot product. Example of calculating the distance from a point to a plane with the usual dot product. Example of calculatin the distance between two skew lines in the space. Example of homothety in the plane. Example of construction of a rotation in the affine plane. Example of construction of a symmetry in the affine space. Two examples of application of pencil of planes.
PART IV. Conics and quadric surfaces.
	Chapter 1. Conics. Example of calculating the tangent to a conic at a point. Example of calculating of tangents to a conic from a exterior point. Three examples of center calculation. Example of calculating the asymprtotic directions and the asymptotes of a hyperbola. Example of calculating the asymptotic directions and the asymptotes of a parabole. Example of calculating the axis and vertex of a parabole. Example of calculating the equation of a conic knowing the center, one focus and the eccentricity. Example of calculating the equation of a hyperbola knowing the focus and a point Example of calculating the equation of a parabole knowing an axis, one directrix line and a point. Example of pencil of conics theought 4 points. Example of calculating the equation of a parabole knowing three points and the tangent at one of them. Example of calculating a conic knowing an asymptote, an axis and a point.

	LINEAR ALGEBRA II es
	Examples in VIDEOS (in Spanish).