The lualinalg package is developed to perform operations on vectors and matrices defined over the field of real or complex numbers inside LaTeX documents. It provides flexible ways for defining and displaying vectors and matrices. No particular environment of LaTeX is required to use commands in the package. The package is written in Lua, and .tex file is to be compiled with the LuaLaTeX engine. It may also save users efforts to copy vectors and matrices from other software (which may not be in LaTeX-compatible format) and to use them in a TeX file. The vectors and matrices of reasonable size can be handled with ease. The package can be modified or extended by writing custom Lua programs.