Posts Tagged ‘matrices’
Friday, October 23rd, 2009
Introduction to the Four-Vector
Description
A detailed tutorial on the four-vector. Step by step tutorial including several examples of the four-vector and how to solve it for reference.
Overview
In linear algebra, a four-vector is defined as a vector in four-dimensional real vector space. The difference between a vector and a four-vector is that a four-vector can be transformed by Lorentz transformations. The concept of four-vectors branches out throughout vector mathematics, and to special relativity and general relativity. The concepts are a little different in each, but not enough to make it confusing if you are learning about them from a different standpoint. Four-vectors are often used in combination with matrices.
Tags: algebra, concept, four-dimensional, four-vector, general, Lorentz, matrices, real, relativity, space, special, transformations, vector
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Thursday, October 15th, 2009
Introduction to the Inverse Matrix
Description
A detailed tutorial on the inverse matrix and how to calculate the inverse matrix. Step by step tutorial including several examples of the inverse matrix for reference.
Overview
All square matrices have an inverse, except for the rare invertible matrices, called singular matrices. The inverse of a square matrix can be defined in mathematical terms as the matrix times the inverse of the matrix is equal to I, which represents the identity matrix. The inverse of a matrix may be found by using the inverse function. This makes the inverse easy to find, as you follow basic rules for finding the inverse of other types of equations.
Tags: algebra, equations, function, identity, inverse, invert, invertible, Math, matrices, matrix, rules, singular, square
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Thursday, October 15th, 2009
Introduction to Singular Matrices
Description
A detailed tutorial on singular matrices. Step by step tutorial including several examples of singular matrices and how to identify singular matrices for reference.
Overview
A singular matrix is a square matrix that is not invertible. In order to not be invertible, the determinant must be zero. No other values will make a matrix singular. Single matrices are very rare – almost all square matrices are invertible. A quick way to find out if a matrix is invertible or singular is to attempt to invert the matrix.
Tags: algebra, degenerate, determinant, invert, invertible, Math, matrices, matrix, rare, singular, square, zero
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Tuesday, September 29th, 2009
How to Use Cramer’s Rule
Description
A detailed tutorial on how to solve systems of equations using Cramer’s rule. Step by step tutorial including several examples of how to solve for systems of equations using Cramer’s rule for reference.
Overview
Cramer’s rule is a theorem in linear algebra that is used as an alternative method of solving systems of equations. Cramer’s rule uses matrices to solve for systems of equations, and is typically used when there is a unique solution. The solution is expressed in the form of matrices which are obtained by replacing one column of the vector of right hand sides of the equations.
Tags: algebra, Cramer's rule, Gabriel Cramer, linear algebra, linear equations, Math, matrices, matrix, systems of equations, unique, vector
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Tuesday, September 8th, 2009
How to Multiply Matrices Using Matrix Multiplication
Description
This video explains the difference between addition/subtraction and multiplication of matrices. It also explains why there is such a difference. Several example problems are provided in the video, along with a clear explanation of the multiplication process.
Overview
Matrix multiplication is very different from addition and subtraction with matrices. Instead of combining the numbers from the same places, you must combine rows from the first matrix with columns from the second matrix. When you are looking for the number for the top left corner – the first number of your matrix – you will look at the top row of the first matrix and the first column of the second matrix. Say you have 2 matrices like this:
{a b} * {w x}
{c d} * {y z}
You will look at a and b, and w and y, to find your first term. The first number of your new matrix will be [(a * w) + (b * y)]. When you want to find the second term – the term still in the first row, but in a different column – you will switch you focus to the other column, while keeping your row of focus the same, and solve it in the same way. This must be done for every term in the matrices.
Tags: linear algebra, Math, matrices, matrix, matrix multiplication, multiplication, multiply
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Tuesday, September 8th, 2009
How to Add and Subtract Matrices
Description
This video explains the different types and sizes of matrices and what makes up each of them. It explains how to match up the sizes so you know if addition is possible. Several sample problems for addition are provided in the video.
Overview
While with normal numbers, you can add anything, some sets of matrices cannot be added. Matrices can only be added when they are the same size. Sizes of matrices are recorded by the numbers that are in each row and colum. For instance, a matrix with 3 rows and 3 columns would be referred to as a 3×3 matrix. If your matrices are the same size, you can add them. You then simply match up the numbers in your matrices to add them. This means that the number in the top right corner of the first matrix is added to the number in the top right corner of the second matrix, and the number they add up to will go in the same place in the matrix that is the solution to the problem. Subtraction works the exact same way as addition.
Tags: addition, algebra, equation, equations, linear algebra, Math, matrices, matrix, set
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Tuesday, September 8th, 2009
An Introduction to Matrices
Description
This video shows how to solve equations, but the most important part of this video is displayed right in the beginning – it converts a regular set of equations into a matrix, which shows you exactly what a matrix is. A sample problem is provided, or you can simply benefit from the conversion process.
Overview
A matrix, the plural of which is matrices, is a set of numbers that form an equation. They come up in many different parts of math, and are used very commonly in Linear Algebra. They make viewing a set of equations much easier. The most important thing to remember about matrices is that everything must line up. Here is an example:
1x + 2y = 18
5x + 7z = 32
Must be rewritten as:
1x + 2y + 0z = 18
5x + 0y + 7z = 32
This way it is lined up correctly when you put it in the matrix. Some matrices have a line before the solution, to seperate it from the other numbers – this is optional. Even if it is not there, the last number is always the solution. So when you put it into a matrix, it will look like this:
{1 2 0 | 18}
{5 0 7 | 32}
Tags: algebra, equation, equations, linear algebra, Math, matrices, matrix, set
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