# MOOC Massive Open Online Courses (Academic Year 2018/2019)

## Slides

 Real number and complex numbers    Power    Roots    Notational conventions in fields    Polynomials Vectors    Equal vectors    Addition of two vectors    Subtraction of two vectors    Coordinates of a vector    Norm of a vector Angle between two vectors    Inner product of vectors    Orthogonal vectors Cross product of vectors    An important formula Definition    Theorem Operations with Matrix    Diagonal matrix    The trace of a square matrix    Scalar multiplication    Identity matrix Definition of linear combination    Definition of linear independence    Bases Definition    Properties    Inverse of a 2x2 matrix    Types of matrices Linear Systems    Homogeneous linear system Definition of determinant    Addition of two rows or columns    Determinants and systems Definition    Examples Extension of Sub-Basis    Solution Definition    Gram-Schmidt process Matrix of a linear transformation    Application Definition    Theorem    Cayley Recall the definition    Eigenspaces    Linear independence of eigenvectors Definition    Theorem Vector form of a straight line    General equation of a line    Mid-point    Perpendicular Bisector    vector equation of a line (I) Distance between two points on the plans    Parametric equations of a circle    Tangent of a circle    Relative positions The parabola    The tangent of the parabola Ellipse    Parametrical equations    Eccentricity    Hyperbola Three dimensional space    Midpoint in 3 dimensions    Straight line Equation of a plane in space    Parametric equation of a plane Intersection of two planes in space    Geometric illustration A cylinder in space    Plane

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