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Subsection 1.1.2 Overview

  • 1.1 Opening

    • 1.1.1 Why norms?

    • 1.1.2 Overview

    • 1.1.3 What you will learn

  • 1.2 Vector Norms

    • 1.2.1 Absolute value

    • 1.2.2 What is a vector norm?

    • 1.2.3 The vector 2-norm (Euclidean length)

    • 1.2.4 The vector p-norms

    • 1.2.5 Unit ball

    • 1.2.6 Equivalence of vector norms

  • 1.3 Matrix Norms

    • 1.3.1 Of linear transformations and matrices

    • 1.3.2 What is a matrix norm?

    • 1.3.3 The Frobenius norm

    • 1.3.4 Induced matrix norms

    • 1.3.5 The matrix 2-norm

    • 1.3.6 Computing the matrix 1-norm and \(\infty\)-norm

    • 1.3.7 Equivalence of matrix norms

    • 1.3.8 Submultiplicative norms

    • 1.3.9 Summary

  • 1.4 Condition Number of a Matrix

    • 1.4.1 Conditioning of a linear system

    • 1.4.2 Loss of digits of accuracy

    • 1.4.3 The conditioning of an upper triangular matrix

  • 1.5 Enrichments

    • 1.5.1 Condition number estimation

  • 1.6 Wrap Up

    • 1.6.1 Additional homework

    • 1.6.2 Summary

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