In this part of the website, we review the key characteristics of matrices and describe how to perform various matrix operations in Excel. We also describe some related topics, such as determinants and the solution of simultaneous linear equations, as well as iterative procedures, such as Newton’s method and Iterative Proportional Fitting Procedure (IPFP). Finally, we show how to use Excel’s built-in iterative methods Goal Seek and Solver.
Topics
- Basic Concepts of Matrices
- Matrix Operations
- Determinants
- Systems of Linear Equations
- Characterizing Solutions to Systems of Linear Equations
- Newton’s Method
- Goal Seeking and Solver
- Excel’s Solver
- Iterative Proportional Fitting Procedure (IPFP)
References
Wikipedia (2013) Single value decomposition
https://en.wikipedia.org/wiki/Singular_value_decomposition
Golub, G. H., Van Loan, C. F. (1996) Matrix computations. 3rd ed. Johns Hopkins University Press
Searle, S. R. (1982) Matrix algebra useful for statistics. Wiley
Perry, W. L. (1988) Elementary linear algebra. McGraw-Hill
Fasshauer, G. (2015) Linear algebra.
https://math.iit.edu/~fass/532_handouts.html
Lambers, J. (2010) Numerical linear algebra
https://www.yumpu.com/en/document/view/41276350
Wikipedia (2014) Newton’s method
https://en.wikipedia.org/wiki/Newton%27s_method