In the wonderful world of mathematics, there is an important and mysterious operation - matrix multiplication, maybe you have encountered this concept in math class, and when you look up and see those square matrices made of numbers, you may have a question in your heart: "What is the mystery of multiplying these numbers?"."Don't worry, let's step into this maze of matrices and uncover the fascinating story behind matrix multiplication.
Basic principles of matrix multiplication
Matrix multiplication is an important operation in linear algebra, unlike the multiplication of numbers we usually see, matrix multiplication involves the operation between two matrices, but it should be noted that not all matrices can multiply each other, in order to multiply two matrices,The number of columns in the first matrix must be equal to the number of rows in the second matrix
Here's an example
For example, we have two matrices, a and b:
Here, a is a 2x2 matrix (2 rows and 2 columns) and b is also a 2x2 matrix, because the number of columns (2) of a and the number of rows (2) of b are the same, so the two matrices can be multiplied.
Steps of matrix multiplication
When multiplying AXBs, you would calculate each element of the result matrix like this:
1.The first element of the result matrix is the result of multiplying the first row of a by the corresponding element of the first column of b, and then adding.
For example, the first element of an AXB is:
2.And so on, you'll do this with every row of A and every column of B, and you'll end up with all the elements of the result matrix.
Complete multiplication results
Therefore, the result of AXB is:
Common mistakes made:
1.The number of columns does not match the number of rows: The most common mistake is multiplying a matrix with a number of columns that does not match the number of rows, and the multiplication can only be done if the number of columns in the first matrix and the number of rows in the second matrix are equal.
2.Wrong way of working: Matrix multiplication is not the multiplication of elements in the same position of two matrices, it is based on the multiplication and accumulation of points of rows and columns.
3.Dissatisfaction with the commutative law: Matrix multiplication does not follow the commutative law, that is, AXB is not equal to BXA.
In the sea of mathematics, matrix multiplication is a bright pearl, shining with abstract and profound light, through this brief exploration, we seem to quietly pass through the complexity of numbers, personally feel the charm of matrix multiplication, whether it is in the field of computer graphics, Physics simulation, or various applications in daily life, matrix multiplication is like a silently dedicated hero, silently supporting everything we rely on, allowing us to continue to explore in this ocean of mathematics and discover more unknown mathematical beauty.