Akademik Dersler - İçerik

Explains the concepts of base and dimension of vector space.
Explains the concept of dimension of a vector space.
Expresses vector spaces in different dimensions.
Explains base concept of a vector space and properties of vectors on the base.
Expresses row and column space of a matrix.
Explains some functions defined between vector spaces.
Expresses required conditions for a transformation in order to be a linear transformation.
Finds kernel and image spaces of a linear transformation.
Expresses some of the algebra operations between linear transformations.
Explains matrix representation of a linear transformation.
Finds the matrix representing a linear transformation.
Finds the image set when a transformation matrix is given.
Expresses base variation matrix.
Explains the relationship between two matrices of a linear transformation calculated with respect to different bases.
Explains under what conditions they represent the same transformation, if two matrices of the same size are given.
Explains eigenvalues and eigenvectors of a linear transformation.
Explains concepts of eigenvalues and eigenvectors of a matrix.
Finds characteristic polynomial, eigenvalues and eigenvectors of a transformation matrix.
Explains when a transformation matrix can be written in the form of a diagonal matrix.
Explains concepts of inner product on vector spaces.
Finds the length of a vector in some vector spaces and the angle between two vectors.
Explains that two vectors are orthogonal.
Expresses that a set is orthogonal and orthonormal.