M3 submachine gunThe M3 is an American .45-caliber submachine gun adopted by the U.S. Army on 12 December 1942, as the United States Submachine Gun, Cal. .45, M3. The M3 was chambered for the same .45 ACP round fired by the Thompson submachine gun, but was cheaper to mass produce and lighter, at the expense of accuracy. The M3 was commonly referred to as the "Grease Gun" or simply "the Greaser," owing to its visual similarity to the mechanic's tool. The M3 was intended as a replacement for the Thompson, and began to enter frontline service in mid-1944.
Row and column spacesIn linear algebra, the column space (also called the range or ) of a matrix A is the span (set of all possible linear combinations) of its column vectors. The column space of a matrix is the or range of the corresponding matrix transformation. Let be a field. The column space of an m × n matrix with components from is a linear subspace of the m-space . The dimension of the column space is called the rank of the matrix and is at most min(m, n). A definition for matrices over a ring is also possible.
Line segmentIn geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry, a line segment is often denoted using a line above the symbols for the two endpoints (such as ).
Matrix ringIn abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication . The set of all n × n matrices with entries in R is a matrix ring denoted Mn(R) (alternative notations: Matn(R) and Rn×n). Some sets of infinite matrices form infinite matrix rings. Any subring of a matrix ring is a matrix ring. Over a rng, one can form matrix rngs. When R is a commutative ring, the matrix ring Mn(R) is an associative algebra over R, and may be called a matrix algebra.
MultiplicationMultiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the quantity of the other one, the multiplier; both numbers can be referred to as factors.
Matrix decompositionIn the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems. In numerical analysis, different decompositions are used to implement efficient matrix algorithms. For instance, when solving a system of linear equations , the matrix A can be decomposed via the LU decomposition.
Ancient Egyptian multiplicationIn mathematics, ancient Egyptian multiplication (also known as Egyptian multiplication, Ethiopian multiplication, Russian multiplication, or peasant multiplication), one of two multiplication methods used by scribes, is a systematic method for multiplying two numbers that does not require the multiplication table, only the ability to multiply and divide by 2, and to add. It decomposes one of the multiplicands (preferably the smaller) into a set of numbers of powers of two and then creates a table of doublings of the second multiplicand by every value of the set which is summed up to give result of multiplication.
