Posts Tagged ‘diagonal’
Friday, December 18th, 2009
Your Guide to Lattice Multiplication
Description
A detailed tutorial on lattice multiplication. Step by step tutorial including several examples of lattice multiplication for reference.
Overview
Lattice multiplication is a method that is used to multiply large numbers. It uses the multiplication of smaller numbers to figure out the product of two larger numbers. Because of this, basic knowledge of times tables is required. Lattice multiplication is compromised of boxes with diagonal lines through them. Draw the diagonal line in each box from the top right corner to the bottom left corner. The top left is for your tens place (the first digit in a two digit number) and the bottom right is for your ones place (the second digit in a two digit number). The number of boxes you have depends on the number you are multiplying – for example, if you are multiplying two one-digit numbers, there is one box. If you are multiplying two 2-digit numbers, there are four boxes. The first number is across the top, and the second down the side. Where each single digit number instersects, multiply them together using the box technique. Then, using the same pattern you drew the diagonals with, mutliply the diagonals. If you have two 2-digit numbers, there will be four diagonals. Multiply together the diagonals to come up with four numbers, and the pattern you use to put them together is going from the top down and then to the right.
Tags: algebra, box, combine, diagonal, digit, double, larger, lattice, multiplication, multiply, single, small, tables, times
Posted in Algebra | No Comments »
Friday, November 13th, 2009
Overview of Negative Slopes
Description
A detailed tutorial on negative slopes. Step by step tutorial including several example problems with negative slopes for reference.
Overview
A negative slope is very similar to a positive slope. It is still in the form of rise over run, and it makes no real difference in an equation if a slope is negative or positive. What it does is change the way you graph it. A positive slope you go up and the to the right. In a negative slope, you will either go up and to the left or down and to the right, depending on if the rise or the run is negative. The main mistake that people make with a negative slope is thinking if they see a negative sign, the slope is definitely negative. This is not true. A negative rise and a negative run actually equals a positive slope, you graph it as going down and going to the left, which still creates a positive slope – and in mathematics, two negatives make a positive.
Tags: diagonal, down, graph, horizontal, left, negative, positive, right, rise, run, slope, up, vertical
Posted in Algebra | No Comments »
Thursday, November 12th, 2009
An Overview of Magic Squares
Description
A detailed tutorial of magic squares. Step by step tutorial including several examples of magic squares for reference.
Overview
Magic squares are a fun mathematical trick and puzzle. It is an arrangement such as 3×3, 4×4, or any other nxn pattern of numbers. Typically a magic square will contain any of the integers between 1 and n^2. Magic squares are set up so that all rows and columns, and both diagonals, add up to the same constant. It does not matter what constant it is, as long as all rows, columns, and diagonals add up to the same one.
Tags: arithmetic, column, constant, diagonal, integer, magic, n!, normal, number, perfect, real, row, square, sum, word
Posted in Arithmetic | 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
Main Diagonal of a Matrix
Description
A detailed tutorial on the main diagonal of a matrix. Step by step tutorial including several examples of main diagonals for reference.
Overview
The main diagonal of a matrix is the diagonal that starts at the top left corner, and continues down and to the right one step until either the other corner is reached (square matrices only), the bottom of the matrix is reached, or the right side of the matrix is reached. The main diagonal is also sometimes called the primary diagonal or the leading diagonal
Tags: algebra, bottom, diagonal, leading, left, linear, main, matrices, matrix, primary, regular, right, square, step, top
Posted in Algebra | No Comments »
Thursday, November 5th, 2009
Using Tally Marks in Equations
Description
A detailed tutorial om how to use tally marks to solve equations. Step by step tutorial including several examples of tally marks for reference.
Overview
Tally marks are a way of counting that most of us were taught about at a young age – where you count to five by drawing four vertical bars with one diagonal line across them. But tally marks can also be used to help with equations, especially ones with addition and subtraction. As a tally mark is a type of counting numeral that gives you a visual example on solving equations, they can be very useful on simple additon and subtraction problems, as it helps to prove the right answer has been found.
Tags: arithmetic, bar, bars, count, counting, diagonal, five, five-bar, gate, horizontal, lines, numbers, numerals, tally marks, vertical, visual
Posted in Arithmetic | No Comments »
Thursday, November 5th, 2009
Transpose of a Matrix Explained
Description
A detailed tutorial on the transpose of a matrix. Step by step tutorial including several examples of the transpose of a matrix for reference.
Overview
When you transpose a matrix, it is simply a way of saying that you write the matrix in a different way – this creates a new matrix. There are three ways you can transpose a matrix. The first way is to write the rows of your matrix as columns instead. The second way is to write the columns of your matrix as rows instead. And the third way is to reflect your matrix by its main diagonal. All of these actions accomplish the same thing, so it does not matter which method you use. When people talk about transposing something, they are usually referring to matrices.
Tags: algebra, columns, diagonal, element, equivalent, main, matrices, matrix, method, reflect, rows, scalar, transpose
Posted in Algebra | 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 »
Tuesday, November 3rd, 2009
How to Find the Trace
Description
A detailed tutorial on find the trace of a matrix. Step by step tutorial including several examples of how to find the trace for reference.
Overview
The trace of a square matrix is defined to be the sum of the elements on the main diagonal of the matrix. This can be mathematically expressed as:
Remember, the trace is only defined for square matrices – not any other kind of matrix.
Tags: algebra, diagonal, eigenvalue, element, invariant, linear, main, matrices, matrix, Spur, square, sum, trace
Posted in Algebra | 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 »
