Akademik Dersler - İçerik

express the set of vectors in euclidean spaces is a vector space.
express addition and scalar mutiplication operations.
express some properties of addition and scalar mutiplication operations.
express the set of vectors in euclidean spaces is a vector space.
generalize the concepts of a real (complex) vector space to an arbitrary finite-dimensional vector space.
define a vector space and subspace of a vector space.
explain properties of R^n and subspaces of R^n.
determine whether a subset of a vector space is linear dependent.
describe the concept of a basis for a vector space.
investigate properties of vector spaces and subspaces using by linear transformations.
express linear transformation between vector spaces.
represent linear transformations by matrices.
explain what happens to representing matrices when the ordered basis is changed.
describe the concepts of eigenvalue, eigenvector and characteristc polynomial.
determine whether a linear transformation is diagonalizable or not.
generalize the concept of a real (copmlex) inner product space to an arbitrary inner product space.
express the concepts of an inner product space and an orthonormal basis.
apply the gram-schmidt process to construct an orthonormal basis for a space.
analyse diagonalizable for symmetric and hermitian transformations.
explain the concept of quadratic form.