Algebra of Matrices

With the vocabulary of matrices in place, we can now define arithmetic on them, mirroring what you already know for ordinary numbers. This section covers four operations: multiplying a matrix by a scalar, adding two matrices, subtracting one matrix from another, and multiplying two matrices together. Each operation comes with its own conditions on the order (shape) of the matrices involved, and its own set of properties — some familiar from ordinary arithmetic, some not (matrix multiplication, in particular, behaves quite different …