Linear Algebra
Linear Algebra is that branch of mathematics that helps us understand coordinates & plane visualizations by performing algebraic operations.
The representation of coordinates and planes is done by matrices, points & vectors.
Why Linear Algebra in Machine Learning?
Linear Algebra relates variables(Dependent Variables, Independent Variables, and Target Variables) by a mathematical relationship which becomes a function and easily predictable.
Some Basics Concepts of Linear Algebra-
Simple Linear Equations- These are the first steps which we all somehow have worked with (even a non-mathematics background guy). This establishes the basic relationship between two variables by a linear line.
Linear Line-A line with constant slope throughout.
The above equation is x=y , on every coordinate x is equal to y.
Let’s take a little complex equation.
y = x -1
There’s just a -1 one in the independent variable side look the graph shifted downward. This establishes that now y is equal to a value less in x.
Matrix
A matrix is an arrangement of elements in rows and columns. These elements can be anything real numbers, imaginary numbers, Variables, constants literally anything.
Matrices are multi-discipline shared concept from mathematics to computer science. But the basic idea is the same of multiple arrangements in row and column.
Order of Matrix is defined as the number of rows and columns.
Order of a matrix is = Number of rows × Number of columns
Identity Matrix is defined as the matrix with diagonal elements as unity and all others as zero or in a more technical definition where row and column is equal that element is one all others are zero.
Vector
A vector is a multi dimensional implementation of coordinates. A vector carries both magnitude and direction(old-school definition).
The intersection of x and y points and a path to that intersectional point is a vector.
On moving 3 units on y-axis and 4 points on x-axis the intersection to both the points from the origin is the resultant vector. Or you can say the projection of 3 units of y to 4 units of x.