Posts Tagged ‘identity’
Tuesday, December 29th, 2009
How to Construct a Cayley Table
Description
A detailed tutorial on how to construct a Cayley table. Step by step tutorial including several examples of how to construct a Cayley table for reference.
Overview
A Cayley table is a table that expresses the structure of a finite set. A Cayley table is set up by having the elements of the set across the first row, and numbers going in a numerical order of n + 1 starting at 1 down the first column. Sometimes the table is simply different ways the elements can be ordered. Other times is is a true table, where an operation is performed between two numbers in the space where they cross each other. However, a true Cayley table must be constructed using an identity skeleton. Once an identity skeleton for the finite set has been decided on, the Cayley table can be filled out using the identity skeleton. Since there is more than one possible identity skeleton for a finite set, you may have to go through a trial and error process until you find the right one.
Tags: addition, Cayley, chart, column, cross, discrete math, division, elements, error, finite, graph, identity, multiplication, operation, order, process, row, set, skeleton, subtraction, table, trial
Posted in Discrete Math | No Comments »
Thursday, November 19th, 2009
Overview of the Additive Identity
Description
A detailed tutorial on how to solve equations using the additive inverse. Step by step tutorial including several examples of how to solve equations with the additive inverse for reference.
Overview
The additive inverse is the inverse of the additive identity – which should be very easy to guess. However, the problem is not guessing the definition of the additive inverse – the problem is knowing what the inverse of the additive identity is. The additive identity states that any number plus zero equals itself. The additive inverse states that any positive number minus its true value or any negative number plus its true value is equal to zero – in other words, that two inverses together equal zero. You solve equations by using the additive inverse.
Tags: add, additive, arithmetic, basic, divide, equations, identity, inverse, itself, multiply, nothing, plus, property, same, subtract, zero
Posted in Arithmetic | No Comments »
Thursday, November 19th, 2009
Overview of the Additive Identity
Description
A detailed tutorial on the additive identity. Step by step tutorial including several examples of the additive identity for reference.
Overview
The additive identity is very similar to the zero properties of multiplication and addition. However, the additive property is only used with addition – which should be easy to tell from the name of this identity. The additive identity states that any number plus zero, or with zero added to it, is equal to itself. The additive property is one of the properties that all teachers expect you to already know, so it is important to learn it.
Tags: add, additive, arithmetic, basic, divide, identity, itself, multiply, nothing, plus, property, same, subtract, zero
Posted in Arithmetic | No Comments »
Tuesday, November 10th, 2009
Identifying Zero Polynomials
Description
A detailed tutorial on identifying zero polynomials. Step by step tutorial including several examples of identifying zero polynomials for reference.
Overview
A zero polynomial is the additive identity of an additive group of polynomials. So this means it is not a unique polynomial, even though it may seem like it. In order to identify a zero polynomial, you need to be aware of the two properties that zero polynomials possess. The first one is that all coefficients of a zero polynomial are zero, and add up to zero. The second is that a zero polynomial doesn’t have a degree – it is an undefined degree. Typically people will write this as a degree of -1, or more common, of negative infinity.
Tags: addition, additive, algebra, coefficient, degree, group, identity, infinity, negative, one, polynomial, properties, property, undefined, zero
Posted in Algebra | No Comments »
Friday, November 6th, 2009
Identity Matrix Explained
Description
A detailed tutorial on the identity matrix. Step by step tutorial including several examples of the identity matrix and how to solve it for reference.
Overview
An indentity matrix is a matrix that is said to be of size n. It is considered to be the n-by-n square matrix with ones on the main diagonal and zeros elsewhere. The identity matrix is denoted as the variable I. The identity matrix has some extremely important properties of its own, especially multiplication properties. It is a unique type of matrix that is found rarely, but is used very often in several different branches of math.
Tags: -1, 0, algebra, diagonal, i, identity, linear, main, matrices, matrix, multiplication, one, properties, square, uniquem, variable, zero
Posted in Algebra | No Comments »
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
Posted in Algebra | No Comments »
Friday, October 9th, 2009
Definition of a Semiperimeter
Description
A detailed tutorial of what a semiperimeter is. Step by step tutorial including a visual example of a semiperimeter for reference.
Overview
In geometry, a semiperimeter of a polygon (squares, rectangles, triangles, or any closed and none-rounded shape) is simply half a perimeter – like a radius would be for a circle, almost. If you already have the perimeter of the figure, you can easily obtain the semiperimeter by dividing it in half. The semiperimeter is given its own seperate variable and identity because it is used sometimes in mathematical equations, such as Heron’s formula.
Tags: divide, Geometry, Heron's Formula, identity, Math, perimeter, polygon, semiperimeter, side, variable
Posted in Geometry | No Comments »
