Titlebook: Linear Algebra; J?rg Liesen,Volker Mehrmann Textbook 2015 Springer Nature Switzerland AG 2015 Linear Algebra.Matrices.Echelon Form.Gaussia

Pudendal-Nerve

Textbook 2015inating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear m

Infirm

expository

The Echelon Form and the Rank of Matrices,chelon form is, in some sense, the “closest possible” matrix to the identity matrix. This form motivates the concept of the rank of a matrix, which we introduce in this chapter and will use frequently later on.

Insulin

Vector Spaces,es of certain (namely, finite dimensional) vector spaces can be studied in a transparent way using matrices. In the next chapter we will study (linear) maps between vector spaces, and there the connection with matrices will play a central role as well.

Opponent

Cyclic Subspaces, Duality and the Jordan Canonical Form,he essential properties of . will be obvious from its matrix representation. The matrix representation that we derive is called the Jordan canonical form of .. Because of its great importance there have been many different derivations of this form using different mathematical tools.

hardheaded

1615-2085 r first contact with abstract concepts.Analyzes detailed exaThis self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applic

Apraxia

Fallibility

Linear Maps,nal vector spaces every linear map can be represented by a matrix, when bases in the respective spaces have been chosen. If the bases are chosen in a clever way, then we can read off important properties of a linear map from its matrix representation. This central idea will arise frequently in later chapters.

小溪

Linear Forms and Bilinear Forms,ns. They will also be essential for the further developments in this book: Using bilinear and sesquilinear forms, which are introduced in this chapter, we will define and study Euclidean and unitary vector spaces in Chap.?.. Linear forms and dual spaces will be used in the existence proof of the Jordan canonical form in Chap.?..

BLA

Euclidean and Unitary Vector Spaces,l and complex vector spaces. This, in particular, leads to the idea of orthogonality and to orthonormal bases of vector spaces. As an example for the importance of these concepts in many applications we study least-squares approximations.