After studying this chapter you will be able to
• apply basic operations to vectors and matrices;
• define a vector space;
• define a subspace of a vector space;
• compute the rank of a matrix;
• list the four fundamental subspaces defined by a linear transformation;
• compute the inverse, determinant, eigenvalues, and eigenvectors of a square matrix.
• describe what positive-definite matrices are;
• compute some important matrix decompositions, such as the eigenvalue decomposition, the singular-value decomposition and the QR factorization;
• solve linear equations using techniques from linear algebra;
• describe the ...