Linear Algebra

Misc

Packages
- {sparsevctrs} - Sparse Vectors for Use in Data Frames or Tibbles
  - Sparse matrices are not great for data in general, or at least not until the very end, when mathematical calculations occur.
  - Some computational tools for calculations use sparse matrices, specifically the Matrix package and some modeling packages (e.g., xgboost, glmnet, etc.).
  - A sparse representation of data that allows us to use modern data manipulation interfaces, keeps memory overhead low, and can be efficiently converted to a more primitive matrix format so that we can let Matrix and other packages do what they do best.
- {quickr} - R to Fortran Transpiler
  - Only atomic vectors, matrices, and array are currently supported: integer, double, logical, and complex.
  - The return value must be an atomic array (e.g., not a list)
  - Only a subset of R’s vocabulary is currently supported.
```
#>  [1] !=        %%        %/%       &         &&        (         *        
#>  [8] +         -         /         :         <         <-        <=       
#> [15] =         ==        >         >=        Fortran   [         [<-      
#> [22] ^         c         cat       cbind     character declare   double   
#> [29] for       if        ifelse    integer   length    logical   matrix   
#> [36] max       min       numeric   print     prod      raw       seq      
#> [43] sum       which.max which.min {         |         ||
```

Resources

See Matrix Cookbook pdf in R >> Documents >> Mathematics
- derivatives, inverses, statistics, probability, etc.
Link - A lot of matrix properties as related to regression, covariance, coefficients, etc.
EBOOK statistical linear algebra: basics, transformations, decompositions, linear systems, regression - Matrix Algebra for Educational Scientists
Video Course: Linear Algebra for Data Science - Basics, Least Squares, Covariance, Regression, PCA, SVD

Matrix Multiplication

Matrix Algebra

An expected value equation (VC stands for variance-covariance in example) multiplied by a matrix, C.
- C is factored out of an expected value as C
- C is factored out of a transpose as CT

Factorization