Posts Tagged ‘determinant’
Friday, November 6th, 2009
Introduction to Invariants
Description
A detailed tutorial on invariants and the property of invariance. Step by step tutorial including several examples of invariants for reference.
Overview
Invariants are any function or number that displays the property of invariance. Invariance is when a function or number can go through several transformations without changing, or without going outside of its set parameters. The set parameters differ depending on the function or number. Some examples of invariant functions and numbers are the absolute value of a complex number, the degree of a polynomial, and certain parts of a square matrix
Tags: absolute, arithmetic, complex, degree, determinant, eigenvalue, eigenvector, function, invariance, invariant, matrix, number, parameters, polynomial, square, trace, transformations, value
Posted in Arithmetic | No Comments »
Tuesday, November 3rd, 2009
How to Find the Determinant
Description
A detailed tutorial on how to find the determinant. Step by step tutorial including several examples of finding the determinant for reference.
Overview
The determinant is a number that is associated with a square matrix. In a mathematical sense, the determinant is a scale factor for measure when the matrix is regarded as a linear transformation. The determinant is denoted by two bars on either side of the matrix, which can be confused with the absolute value of the matrix. The determinant is found by subtracting the products of the diagonals of the matrix, at least in a 2×2 matrix.
Tags: absolute, algebra, determinant, diagonal, factor, linear, matrices, matrix, product, scale, square, subtract, transformation, value
Posted in Algebra | No Comments »
Tuesday, November 3rd, 2009
Rule of Sarrus Explained
Description
A detailed tutorial on the Rule of Sarrus. Step by step tutorial including several examples of the Rule of Sarrus and determinants for reference.
Overview
The Rule of Sarrus is a method used to compute the determinant of a 3×3 matrix. Mathematically stated, if you are given a 3×3 matrix, you can compute the determinant by repeating the first two columns of the matrix behind the third column, so that you have 5 columns in a row. This forms a 3×5 matrix. Then you add the products of the diagonals going from top to bottom (left to right), and subtract the products going from bottom to top (left to right). This can also be used for 2×2 matrices, but the rule used is a little different.
Tags: 2x2, 3x3, 3x5, add, algebra, bottom, column, determinant, diagonal, left, matrices, matrix, product, right, row, rule, sarrus, scheme, subtract, top
Posted in Algebra | No Comments »
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
Posted in Algebra | No Comments »
