**2**

Linear algebra

**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 ...

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