What is linear algebra?
Many difficult problems can be handled easily once relevant information is organized in a certain way.
In this post, we will be focusing on linear algebra, it’s applications and uses in the sciences, engineering and programming.
Now let’s talk about linear algebra.
So what is linear algebra?.
In my own words, it is the study of vectors and linear functions.
It includes the study of lines, planes, and subspace but is also concerned with properties common to all vector spaces.
For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations.
Also, functional analysis may be basically viewed as the application of linear algebra to spaces of functions.
Linear algebra can be applied in most sciences and engineering fields, because it allows modeling many natural phenomena, and efficiently computing with such models.
For nonlinear systems, which cannot be modeled with linear algebra, it is often used as a first-order approximation.
Linear algebra is about linear combinations.
That is, using arithmetic on columns of numbers called vectors and arrays of numbers, normally referred to as matrices, to create new columns and arrays of numbers.
In linear algebra, you have to find the unknowns in systems of linear equations.
A linear equation is a series of terms and mathematical operations where some terms are unknown.
Why linear algebra is Important?.
It is vital in multiple areas of science in general because, linear equations are easy to solve, practically in every area of modern science.
Here are some of the linear algebra applications:
1. Ranking in Search Engines
One of the most important use of linear algebra is in the creation of google. The most complicated ranking algorithm is created with the help of linear algebra.
2. Signal Analysis
It is massively used in encoding, analyzing and manipulating the signals that can be either audio, video or images etc.
3. Linear Programming
Optimization is an important application of linear algebra which is widely used in the field of linear programming.
4. Error-Correcting Codes
It is used in coding theory. If an encoded data is tampered with a little bit and with the help of linear algebra it should be recovered. One such important error-correcting code is called hamming code.
Predictions of some objects should be found using linear models which are developed using linear algebra.
6. Facial Recognition
An automated facial recognition that uses linear algebraic expression is called principal component analysis.
An important part of graphics is projecting a 3-dimensional scene on a 2-dimensional screen which is handled only by linear maps which are explained by linear algebra.
They can be used to reduce the dimensionality of a data set, using a technique called Principal Component Analysis (PCA), which can be an initial step before applying other machine learning techniques. That is probably one of the purest applications of linear algebra in machine learning.
9. Framing Optimization Algorithms
Linear algebra is a practical way to frame optimization algorithms within a computer, it is basically solving linear systems of constraints.
Now that we have outlined all the applications, let’s come to machine learning.
Applications of Linear Algebra in Machine Learning
So how is linear algebra used in machine learning?.
Linear algebra can be used to process data to accomplish tasks, such as:
- Graphical transformations
- Face morphing
- Object detection and tracking
- Audio and image compression
- Edge detection
- Signal processing
Linear algebra works as a computation engine in machine learning.
Most machine learning algorithms use a classifier, and train it by minimizing error between the value calculated by the nascent classifier and the actual value from the training data.
This can be done iteratively.
If the latter, then the technique is usually SVD or some variant.
In data handling system, a lot of data is handled and all of the techniques in current use involve some type of matrix decomposition, a fundamental class of linear algebra techniques.
It is very difficult to deal with large data so many techniques have been proposed to compress the data which are based on linear algebra. Principal component analysis is one of many techniques.
There are many applications of linear algebra in machine learning and computer science, from single circuit solving to large web engine algorithms.
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