Finding the Matrix O for a 4x4 Operator Acting on a 4x1 Vector

In summary, a matrix is a rectangular array of numbers or symbols used to represent and manipulate data in mathematics and science. To find the matrix of a given set of data, the data must be organized into rows and columns. The purpose of finding a matrix is to make data analysis and manipulation easier, and it can be used in research for a variety of purposes, such as modeling complex systems and solving equations. There are also various tools and software available to assist with finding and using matrices, including spreadsheet programs and statistical analysis software.
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MrMuscle
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TL;DR Summary
I have a vector A, and when I apply operator O on it, I get vector B.
I know A and B, but don't know how to find O.
I have a 4x4 operator O. I apply it on a 4x1 vector A. Let's say A =[0.7; 0.4 ; 0.4; 0.3]. When O acts on A, I get B.

Let's say B=[0.74 ; 0.56; 0.08 ; 0.36]. The problem is I don't know how to find O. Can you please help me. My basis are [1 ; 0 ; 0; 0], [0;1 ; 0 ;0] ... and so on.

Thanks in advance!
 
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  • #2
You need to know the results for another three linearly independent vectors in order to determine O uniquely.
 
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1. What is a matrix?

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is commonly used in mathematics and computer science to represent and manipulate data.

2. How can I identify a matrix?

A matrix can be identified by its dimensions, which are denoted by the number of rows and columns. For example, a matrix with 3 rows and 4 columns is referred to as a 3x4 matrix. Matrices are also typically enclosed in brackets [ ] or parentheses ( ).

3. How do I find the inverse of a matrix?

To find the inverse of a matrix, you can use the inverse matrix formula or a calculator. The inverse of a matrix A is denoted as A-1 and it has the property that when multiplied by A, it results in the identity matrix, which is a square matrix with 1s along the main diagonal and 0s elsewhere.

4. What is the purpose of finding a matrix?

Matrices are used in various fields of science and engineering to represent and solve systems of equations, perform transformations, and analyze data. They are also used in computer graphics and machine learning algorithms.

5. How can I solve a matrix equation?

To solve a matrix equation, you can use various methods such as row operations, Gaussian elimination, or matrix inversion. The goal is to transform the matrix equation into an equivalent form where the solution can be easily determined. It is important to keep track of the operations performed on the matrix to ensure the solution is accurate.

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