FUNDAMENTATION OF LINEAR ALGEBRA

 

• Vectors
• Vector Spaces
• Subspaces of the Vector Space
• Linear Dependence of Vectors. Basis of the Vector Space.
• Scalar Product
• Norm of a Vector
• Orthogonal Vectors
• Matrices
• Notation of a Matrix and Operations with Matrices
• Band Matrices and Block Matrices
• Determinants
• Four Subspaces of a Matrix
• Eigenvalues and Eigenvectors of a Matrix
• Schur's Decomposition
• Norms and Condition Numbers of a Matrix
• Cayley-Hamilton Theorem
• Functions of Matrixes