Free Waterproof Fire Starter [VERY LIMITED SUPPLY]

I just got word that we have 1923 of these in the warehouse that they are going to let me give away exclusively to 5000 readers.

This is the [COOLEST little lighter] you've ever seen:



[Click here to claim yours now.]

Remember there are 105698 people on the 5000 list getting this email. Last time I had these to giveaway they were ALL claimed in just a couple of hours.

So if you snooze you lose.[Better go get em while you can.]

P.S. This thing can sit in water for 24 hours and still fire up.[Click here to claim yours now.]











 

Provided that they have the same size (each matrix has the same number of rows and the same number of columns as the other), two matrices can be added or subtracted element by element (see Conformable matrix). The rule for matrix multiplication, however, is that two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second (i.e., the inner dimensions are the same, n for an (m×n)-matrix times an (n×p)-matrix, resulting in an (m×p)-matrix. There is no product the other way round, a first hint that matrix multiplication is not commutative. Any matrix can be multiplied element-wise by a scalar from its associated field. The individual items in an m×n matrix A, often denoted by ai,j, where i and j usually vary from 1 to m and n, respectively, are called its elements or entries. For conveniently expressing an element of the results of matrix operations the indices of the element are often attached to the parenthesized or bracketed matrix expression; e.g.: (AB)i,j refers to an element of a matrix product. In the context of abstract index notation this ambiguously refers also to the whole matrix product. A major application of matrices is to represent linear transformations, that is, generalizations of linear functions such as f(x) = 4x. For example, the rotation of vectors in three-dimensional space is a linear transformation, which can be represented by a rotation matrix R: if v is a column vector (a matrix with only one column) describing the position of a point in space, the product Rv is a column vector describing the position of that point after a rotation. The product of two transformation matrices is a matrix that represents the composition of two transformations. Another application of matrices is in the solution of systems of linear equations. If the matrix is square, it is possible to deduce some of its properties by computing its determinant. For example, a square matrix has an inverse if and only if its determinant is not zero. Insight into the geometry of a linear transformation is obtainable (along with other information) from the matrix's eigenvalues and eigenvectors. Applications of matrices are found in most scientific fields. In every branch of physics, including classical mechanics, optics, electromagnetism, quantum mechanics, and quantum electrodynamics, they are used to study physical phenomena, such as the motion of rigid bodies. In computer graphics, they are used to manipulate 3D models and project them onto a 2-dimensional screen. In probability theory and statistics, stochastic matrices are used to describe sets of probabilities; for instance, they are used within the PageRank algorithm that ranks the pages in a Google search. Matrix calculus generalizes classical analytical notions such as derivatives and exponentials to higher dimensions. Matrices are used in economics to describe systems of economic relationships.