These resources were created by the Department of Economics at the University of Warwick, with funding from the Royal Economic Society. Hosted by the Economics Network
You should be able to
Optionally, also see if you can apply these skills to an economic application or look at the additional resources and advanced quizzes at the bottom of the page,
\(n\times m\) matrix has \(n\) rows and \(m\) columns, \(A_{i,j}\) is entry in row \(i\) and column \(j\),
\(A'=A^T\) is the transpose. \(|A| = \det A\) is the determinant, \(I_n\) is the identity matrix, \(0_{n\times m}\) is the zero matrix,
\(\mathrm{tr}(A)\) is the trace, \(A^{-1}\) is the inverse
Matrix addition and scalar multiplication are component-wise.
\(AB\) is defined if \(A\) is \(n\times m\) and \(B\) is \(m \times k\). The result \(AB\) is \(n\times k\).
To find the \((i,j)^{th}\) entry of \(AB\), take the scalar product of the \(i^{th}\) row of \(A\) and the \(j^{th}\) column of \(B\).
This is the first, of a sequence of applications, explaining how matrices can be used to represent the dynamic change in a labour market, in terms of the distribution of workers across labour market states (employment, unemployment, non-participation). In particular, it is demonstrated how the complex transitional dynamics in the market can be represented succinctly by the means of a dynamic equation involving matrices. The discussion requires conceptual understanding of matrices and matrix multiplication.
The following quiz allows you to test your understanding of using matrices to represent dynamic change in a simplified model of a labour market with two states only.
You can find practice quizzes on each topic in the links above the tutorial videos, or you can take the diagnostic quiz as many times as you like to. If you want to test yourself further, then try the advanced quiz linked below.
Advanced quiz 5.1 Further links and resources 5