Matrix TheoryWorld Scientific, 1991 - 308 lappuses This book provides an introduction to matrix theory and aims to provide a clear and concise exposition of the basic ideas, results and techniques in the subject. Complete proofs are given, and no knowledge beyond high school mathematics is necessary. The book includes many examples, applications and exercises for the reader, so that it can used both by students interested in theory and those who are mainly interested in learning the techniques. |
Saturs
Matrices and linear equations | 1 |
Vector spaces and linear maps | 45 |
The equivalence of all norms in R and in c | 113 |
Jordan canonical form and applications | 141 |
Proof of the Jordan form theorem | 178 |
Perturbation theory | 229 |
Further topics | 252 |
References and further reading | 290 |
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1x1 blocks algebraic multiplicity B₂ calculation characteristic polynomial coefficients column vector completes the proof complex numbers converges corresponding defined definition denoted Determine diagonal entries diagonal matrix diagonalizable differential equations dimension eigenvalues eigenvector element Euclidean norm Example exists function geometric multiplicity Hence hermitian form hermitian matrix inequality inner product invertible matrix Jordan block Jordan form Lemma linear equations linear map linearly independent lower triangular matrix with entries minimal polynomial nilpotent non-singular non-zero vector norm on F nxn matrix obtain operator norm orthogonal orthogonal matrix orthonormal P'AP P¹AP perturbed positive-definite properties Proposition Let prove quadratic form rank real entries real symmetric respect scalar multiplication Schur canonical form sequence Show similar solution set solving subspace symmetric bilinear form system Ax system of linear tends to infinity unique solution unitary matrix upper triangular v'Av v₁ v₂ variables vector space write yields zero vector