Abstract
Notation for a matrix, where a ij is the element in the ith row and the jth column. The matrix has order m × n. If m = n, the matrix is square of order n. An upper triangular matrix. (All elements below the diagonal are 0.) The transpose of A(see (19.11)) is called lower triangular.
Keywords
- Linear Transformation
- Generalize Inverse
- Matrix Norm
- Lower Triangular
- Penrose Inverse
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References
Most of the formulas are standard and can be found in almost any linear algebra text, e.g. Fraleigh and Beauregard (1995) or Lang (1987). See also Sydsæter and Hammond (2005) and Sydsæter et al. (2005). For (19.26)–(19.29), see e.g. Faddeeva (1959). For generalized inverses, see Magnus and Neudecker (1988). A standard reference is Gantmacher (1959).
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Sydsæter, K., Strøm, A., Berck, P. (2010). Matrices. In: Economists’ Mathematical Manual. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28518-2_19
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DOI: https://doi.org/10.1007/978-3-540-28518-2_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26088-2
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