"Linear Algebra and its Applications"-matrix operations

It can be said that the first chapter "Linear Algebra and its Applications" focuses on the relationship between several core concepts (vectors, matrices and linear equations) in linear algebra (the same solution of equations), then the following book begins to introduce these core concepts separately, For example, from this article, we will briefly introduce the content of the matrix.

First of all, we define the computational tools (matrices), we need to study its operation law, this method in the definition of many new operational symbols are applicable. The addition and subtraction of matrices there is no need to talk about, very good understanding, in this article we mainly discuss the matrix multiplication operation of the definition process.

In fact, whether from a discrete point of view or in linear algebra, the law of matrix multiplication always seems so abrupt. The operation of matrix multiplication seems to be innate and illogical, but is it true? Read the reader to do enough careful will find the author in the introduction of the first chapter of the derivation matrix multiplication buried the foreshadowing.

The author once introduced that: the product of matrix A and vector x is natural derivation, we can deduce the algorithm of matrix multiplication, the derivation process is as follows:

You can see that the product of matrix A and n x p of m x n will get a matrix of M x p, whereas for the first column of M x p The matrix is AB1, where B1 is the 1th column vector of Matrix B, it is clear that matrix A should be split into M-line vectors, Then the n components of each line vector AI and the n components of the B1 vector are multiplied and added (this is the multiplication of the matrices and vectors previously defined by us), and the first element of the 1th column of the matrix of M x p is obtained.

"Linear Algebra and its Applications"-matrix operations