What is the View-Projection Matrix?

The View-Projection Matrix (VP Matrix) is just the View Matrix and Projection Matrix multiplied together:

ViewProjection = Projection * View

Note: Matrix multiplication is not commutative:- A * B ≠ B * A
The multiplication order depends on the graphics system, influenced by its row/column major layout and handedness.

This combined matrix allows you to transform a world-space position directly into clip space in one step. Instead of first applying the view matrix, then the projection matrix separately, both transformations are handled at once:

clipSpacePos = worldSpacePos * ViewProjection

That takes a position straight from world space into clip space. Because this matrix is used constantly, most engines just precompute it once per frame and cache it in memory.

Even though it’s “just” the product of two matrices, the VP Matrix is the one that usually gets used the most, it represents the full world-to-clip transformation and decides what actually shows up on screen.

For a comprehensive, detailed breakdown of the entire transformation chain (Model, World, View, and Projection), i highly recommended this article by Marco Alamia:
World, View and Projection Transformation Matrices

This is all we’ll cover about the View-Projection matrix for now. The goal isn’t to dive deep into 3D rendering, but to build a clear, working understanding of how it functions at a basic level.