These comprehensive linear algebra summaries contain all the necessary theorems, definitions, proofs, as well as steps to solve certain problems. The topics covered (second year university-level) are Cross Product, Eigenvalues and Eigenvectors, Diagonalization, Differential Equations, Inner Product, Orthogonality in Inner Product Spaces, Gram-Schmidt Process, Orthogonal Matrices, Orthogonal Diagonalization, Quadratic forms, Optimization, Rank and Nullity and Basic Transformations.

Political Science First Year The miracle of South Africa’s Democracy Introduction: South Africa’s history of apartheid has been a wide-spread phenomenon which many people all across the globe and especially in South Africa greatly opposed but it still managed to carry on for more than 40 years. This essay will look at how South Africa managed to end apartheid and enter into a democratic system rather peacefully, which many people call a ‘miracle’. This essay will discuss the processes t...