> While nowadays most people learn linear algebra through the perspective of vectors and transformations, the matrix and determinant are much older than the ide

> While nowadays most people learn linear algebra through the perspective of vectors and transformations, the matrix and determinant are much older than the ideas of vectors in a multi-dimensional space. Determinants, yes. Matrices, no. Matrices were originally invented by Arthur Cayley as a formalism for describing linear transformations. Mathematicians making historical claims ought to cite their sources. Mathematicians should also define what their terms mean, otherwise it's not clear what they're saying. I'm defining matrices as a certain number system which supports operations called "plus" and "times" (for the pedants, a preadditive category). [edit] Secondary sources: If we look here [1], matrices were invented in parallel by Sylvester and Cayley. Cayley invented the notion of a linear transformation first (1845), and in parallel Sylvester developed a notion of "matrix" to study determinants (1850), and then Cayley finally combined the two ideas to form the modern matrix algebra (1858). Therefore the claim that matrices are older than their modern perspective in terms of vectors and transformations isn't true. [1] - https://www.quora.com/Why-and-who-invented-matrices https://www.quora.com/Why-and-who-invented-matrices