Linear algebra is a system of linear equations, where vectors and matrices are used to solve these systems. Linear algebra describes ways to solve and manipulate linear equations. In addition, linear algebra uses notation for describing its behavior, called a matrix. Thus, their coefficients can be stored in a coefficient matrix.

Two matrices can be multiplied with each other even if they have different dimensions, as long as the number of columns in the first matrix is equal to the number of rows in the second matrix. The result of the multiplication, called the product, is another matrix with the same number of rows as the first matrix and the same number of columns as the second matrix.

The multiplication of matrices is not commutative, which means in general that (A⋅B)≠ (B⋅A).

The multiplication of matrices is associative, which means that (A⋅B)⋅C = A⋅(B⋅C)

A projection is a linear transformation.

The function mapping (x,y,z) in three dimensional space to the point (x,y,0) is an orthogonal projection on to the two dimensional x-y plane. This identity function is represented as the matrix projection :

For complete and in-depth review of what Transformation Matrix is, go over to this webpage.