... Final Remarks 469Appendix 10.A MATLAB Code for Example 10.8 469Appendix 10.B MATLAB Code for Example 10.13 470References 472Problems 47311 Numerical Methods for Eigenproblems 48011.1 Introduction ... under-standing concepts such as fast algorithms for digital signal processing (i.e., fast Fourier transforms, and fast convolution algorithms; e.g., see Ref. 4), cryptography and data security, and ... If x ∈ X and a ∈ K, then the product of a and x is ax,andax ∈ X.(V7) If x, y ∈ X,anda ∈ K, then a(x + y) = ax +ay.(V8) If a, b ∈ K,andx ∈ X, then (a + b)x = ax +bx.(V9) If a, b ∈ K,andx ∈ X,...