In Part 2, we will review, summarize, and explain the basics of matrices.
According to G. Strang's "Linear Algebra and Its Applications", the application of matrices is, after all, to find the solution of linear equations by "Gaussian elimination".
Thinking about its application rather than the practice of matrix calculations, "Square Matrix times Column Vector equals to Column Vector", Square matrix x column vector is equal to column vector, but I think it is an important application form.
To give a concrete example
x + y = 3\\
x - y = 1
When displayed in a matrix,
\begin{pmatrix}
1 & 1 \\
1 & -1
\end{pmatrix}
\times
\begin{pmatrix}
x \\
y
\end{pmatrix}
=
\begin{pmatrix}
3 \\
1
\end{pmatrix}
It will be. This is important. There are two unknowns and two equations, which is the basis of the field of matrix application that can be obtained by "Gaussian elimination".
The matrix on the left is the coefficient matrix. Next to it is an unknown column vector. The last is a constant column vector.
Despite linear algebra, there are some interesting things. First of all, what I find interesting is the area where the nature of algebra and the solving of calculations on a computer are in contact.
What is the algebraic nature? The algebraic property I would like to mention here is that it is "cohesive." Algebra is "Algebra" in English, but it was originally the word "aljabr". It seems to be Arabic, but I remember that it has the meaning of "combine into one." Symbolize an unknown and use them to create an equation. The feeling that the equation is organized is aljabr. I think the word Compound in English fits nicely with programmers. There is a concept of "Compound Procedure", but it is a very important idea.
Then, considering what the matrix format looks like, one is the abbreviation notation. A matrix can be a coefficient or an unknown column vector. A column vector is an m x 1 matrix, isn't it? Solving simultaneous equations by mechanically repeating algebraic operations using this matrix notation is the basis of linear algebra.
The row is "row" in English and the column is "column" in English. Column means a stone pillar monument. Vertical depth x horizontal length, row x column. However, vector notation is easy to get confused with. If it is an n-dimensional row vector, it is a 1 × n matrix, If it is an m-dimensional column vector, it is a matrix of m × 1.
The amount is small, but it's important, so that's the end of Part 2.
Continue to next time.
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