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

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Matrix Functions and Systems of Differential Equations, analysis example involves the exponential function of matrices, and we study the properties of this important function in detail. The analysis of chemical reaction kinetics leads to a system of ordinary differential equations, whose solution again is based on the matrix exponential function.

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https://doi.org/10.1007/978-3-319-24346-7Linear Algebra; Matrices; Echelon Form; Gaussian Elimination; Eigenvalues; Linear Maps; Vector Spaces; Poly

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Matrices,ed in this chapter were introduced by Arthur Cayley (1821–1895) in 1858. His article “A memoir on the theory of matrices” was the first to consider matrices as independent algebraic objects. In our book matrices form the central approach to the theory of Linear Algebra.

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Determinants of Matrices,g and important properties. For instance it yields a necessary and sufficient condition for the invertibility of .. Moreover, it forms the basis for the definition of the characteristic polynomial of a matrix in Chap.?..