Engineering analysis: a vector space approach
This text develops a repertoire of analytical tools related to linear spaces, linear transformations, and linear systems, providing students with the facility to investigate new theoretical concepts in several engineering specialties. Also described are a variety of applications, with examples cited throughout the book. The emphasis is on general cases which illustrate basic principles. Carefully chosen special cases are then deduced from them, which further illustrate the main results. Each result is stated as a logical proposition, with proofs which help establish significant techniques. Included are numerous pictorial representations that supplement the topics discussed.
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NORMED VECTOR SPACES
INNER PRODUCT SPACES
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adjoint algebraic algorithm Banach space called Cauchy sequence characteristic polynomial coefficients column complete orthogonal set compute consider the following convergence defined Definition denoted dimensional eigenspace eigenvalue elementary row Exam Example Exer exists Find finite finite-dimensional linear operator following exercise following result functions mapping Hence Hilbert space impulse response matrix inequality inner product space input interpolating polynomial inverse isomorphic linear combination linear difference system linear differential system linear system linear time-invariant difference linear time-invariant system linear transformation linearly independent Lp(T matrix G(s matrix Q(k matrix representation normed vector space null space one-to-one orthogonal projection orthogonal projection operator orthonormal output proof of Prop properties Proposition range space Refer to Figure response matrix G(k row echelon form scalar Show spectral polynomials spectral representation spectrum standard basis subset subspace Suppose theorem time-invariant difference system transfer function matrix transition matrix transition matrix Q(t transpose unique zero-state