Posts Tagged ‘properties’
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, November 5th, 2009
Cancellation Properties of Natural Numbers
Description
A detailed tutorial on cancellation properties of natural numbers. Step by step tutorial including several examples of cancellation properties for reference.
Overview
Cancellation properties of natural numbers state that when two terms are equal to each other, if the same number is being multiplied or added on both terms, you may cancel them out and the terms will still be equal to each other. Knowledge of the cancellation properties is extremely important for simplification of equations and when trying to find the value of a variable. Mathematically stated, the cancellation properties are that if x + z = y + z or xz = yz, then x = y.
Tags: add, arithmetic, cancel, cancellation, equal, multiply, natural, number, out, properties, property, simplification, simplify, term, value, variable
Posted in Arithmetic | No Comments »
Tuesday, November 3rd, 2009
Eigenvalues and Eigenvectors Explained
Description
A detailed tutorial on eigenvalues and eigenvectors. Step by step tutorial including several examples of eigenvalues and eigenvectors for reference.
Overview
Eigenvalues and eigenvectors are related concepts commonly used in linear algebra. More specifically, they are properties of a matrix. They give very important information about a matrix, and are used in matrix factorization. Assuming that a matrix is a diagonal matrix (a square matrix or a similar matrix that you can calculate diagonals on), then the eigenvalues are the numbers on the diagonal and the eigenvectors are the basis vectors to which there numbers refer. You cannot have an eigenvector without an eigenvalue. However, you can have an eigenvalue without an eigenvector.
Tags: algebra, basis, diagonal, eigenvalue, eigenvector, factorization, linear, matrices, matrix, properties, square, transformations, vectors
Posted in Algebra | No Comments »
Thursday, October 29th, 2009
Successor Properties of Natural Numbers
Description
A detailed tutorial on the successor properties of natural numbers. Step by step tutorial including several examples of the successor properties of natural numbers for reference.
Overview
The successor properties are one of eight sets of properties of natural numbers. The successor properties deal with the actual set of natural numbers, not just parts of the set. It especially concerns the placement of the number 1 in the set of natural numbers. As the term successor implied, these properties deal with what numbers are successors of other numbers. They can be proven by the definition of a successor and the set of natural numbers.
Tags: -1, after, arithmetic, follows, natural, number, properties, set, successor, unique, x
Posted in Arithmetic | No Comments »
Tuesday, October 27th, 2009
Definition of a Scalar Triple Product
Description
A detailed tutorial on scalar triple products. Step by step tutorial including several examples of scalar triple products for reference.
Overview
A scalar triple product is a way of applying other multiplication operators to three vectors. Quite often, the scalar triple product is denoted as (a, b, c). It can also be defined as (a b c) = a(b x c). The scalar triple product has three main properties. The first one is that the absolute value of the scalar triple product is the volume of the three dimensional figure that is formed by the three vectors. The second one is the scalar triple product is only zero if the three vectors are linearly independent. The three vectors must lie in the same plane for this to be true. The third one is that the scalar triple product is only positive if all three of the vectors are considered right-handed.
A simple way to write the scalar triple product is to line up the coordinates of the vectors in this form: 
This is the same as saying 
Tags: absolute, algebra, box, coordinates, figure, independent, linear, mixed, multiplication, operator, parallelpiped, positive, product, properties, right-handed, scalar, three-dimensional, triple, value, zero
Posted in Algebra | No Comments »
