>Some languages have fancy syntax that omits the need for braces. But for those that don't, this is clearly an array of 3 arrays of 3 ints. >It's only intuitiv

>Some languages have fancy syntax that omits the need for braces. But for those that don't, this is clearly an array of 3 arrays of 3 ints. >It's only intuitive to think of this as an array of rows given how it's laid out visually. That's often the least important thing when designing a fast library. It's much better to optimize for common operations in your problem to be fast and thus choose the storage layout of a individual matrix instance accordingly (row-major, column-major, triangular, diagonal, block diagonal, band) so your data cache doesn't get tripped up regularily. The actual API for creating new matrices can still be standardized and always the same. You can have the standardized API accept four column vectors for construction just as well. Just document it as such. If you want, you can also represent the different kinds of vectors as different types, so you don't get identification problems that shouldn't exist. Also, lists of vectors are just that and there's no reason to represent both "list" and "vector" as "array". There are reasons to make the API for "vector" richer--especially since that's why the term "vector" was defined in the first place. But for tiny 4x4 matrices, who cares about caching. But 4x4 are a minority use of matrices. Try 4096x4096. As for OpenGL, they chose to keep the internal storage of matrices the same as it was on IRIS GL. That's a good decision for OpenGL and orthogonal to the question of how column vectors of that matrix can be accessed via an API and to the question of how row vectors of that matrix can be accessed via an API and to the question of how matrices can be created via an API. From a mathematics standpoint, a matrix represents a linear map (a map is a function that takes a vector in space V to a vector in space W). It makes sense to be able to use matrix and linear map interchangeably as a user (i.e. use them just like you would call functions).