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 ENGINEERING:LINEAR ALGEBRA FOR DATA ANALYSIS PART1 Vectors and Matrix   Vectors are mathematical objects with two or more components. In data analysis a vector can represent the person with components as height and weight.The components of a vector can be represented as two components in a Cartesian coordinate system ,one along x- axis the other along Y-axis; these will be the x and y components. The original vector can be represented alternatively by its length and the angle it makes with the x- axis.    The components of vector can be represented as multiples of unit vectors called I and j.The same vector can be represented by a different i* and j* unit vectors. This change  in characterisation of a vector is called change in basis; the vector total magnitude and angle remains unchanged.Change in basis is achieved by projection of components of a vector to the unit vectors of new basis. Projection is thus basically how much the component aligns in the new dir...