The basics

• Basic matrix operations. 1) Spreadsheet example; 2) Information on Mdeterm command
• Solving simultaneous equations by inverting a matrix.
• Spreadsheet example - solving simultaneous equations by inverting a matrix;  1) Information on Minverse; 2) Information on Mmult 
• Matlab example - solving simultaneous equations by inverting a matrix

Advanced material

• Solving simulateous equations when inverting a matrix is not practical

           1) a. Gauss Elimination b. Spreadsheet example
           2) Gauss-Jordan
           3) Difference between Gauss Elimination and Gauss Jordan method (youtube video)
           4) Jacobi method and Gauss-Seidel method (both are iteration methods)

• What if the matrix algorithm complains the matrix cannot be inverted?

           1) What are singular matrices? The vectors are not linearly independent! Usually, this means the equations are some multiple of each other.
           2) Handling singular matrices in Matlab

• Why do we care about this in meteorology? A few examples (of many)

           1) Advanced matrix solutions are used for blending observations with a model to generate an analysis field. Example of the gory details in WRF
           2) Pattern algorithms (Empirical Orthogonal Functions, Principal Component Analysis)
           3) Multiple linear regression algorithms