Items in Algebra

1. Algebra(Verb-Trans.) to receive or obtain from a source or origin

2. AlgebraIn mathematics, a function f defined on some set X with real or complex values is called bounded if the set of its values (its image) is bounded. In other words, there exists a real number M such that |f(x)|≤M for all x in X. A function that is not bounded is said to be unbounded. If f is real-valued and f(x)≤A for all x in X, then the function is said to be bounded (from) above by A. If f(x)≥B for all x in X, then the function is said to be bounded (from) below by B. A real-valued function is bounded if and only if it is bounded from above and below. An important special case is a bounded sequence, where X is taken to be the set ℕ of natural numbers. Thus a sequence f=(a0,a1,a2,…) is bounded if there exists a real number M such that |an|≤M for every natural number n. The set of all bounded sequences forms the sequence space l∞. The definition of boundedness can be generalized to functions f:X→Y taking values in a more general space Y by requiring that the image f(X) is a bounded set... from wikipedia.org

3. AlgebraIn elementary algebra, a trinomial is a polynomial consisting of three terms or monomials. == Examples of trinomial expressions == 3x+5y+8z with x,y,z variables 3t+9s2+3y3 with t,s,y variables 3ts+9t+5s with t,s variables ax2+bx+c, the quadratic polynomial in standard form with a,b,c variables. Axaybzc+Bt+Cs with x,y,z,t,s variables, a,b,c nonnegative integers and A,B,C any constants. Pxa+Qxb+Rxc where x is variable and constants a,b,c are nonnegative integers and P,Q,R any constants. == Trinomial equation == A trinomial equation is a polynomial equation involving three terms. An example is the equation x=q+xm studied by Johann Heinrich Lambert in the 18th century. === Some notable trinomials === The quadratic trinomial in standard form (as from above): ax2+bx+c sum or difference of two cubes: a3±b3=(a±b)(a2∓ab+b2) A special type of trinomial can be factored in a manner similar to quadratics since it can be viewed as a quadratic in a new variable (xn below). This form is factored as: x2n... from wikipedia.org

4. AlgebraIn geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product. == Scalar triple product == The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two. === Geometric interpretation === Geometrically, the scalar triple product 𝐚⋅(𝐛×𝐜) is the (signed) volume of the parallelepiped defined by the three vectors given. === Properties === The scalar triple product is unchanged under a circular shift of its three operands (a, b, c): 𝐚⋅(𝐛×𝐜)=𝐛⋅(𝐜×𝐚)=𝐜⋅(𝐚×𝐛) Swapping the positions of the operators without re-ordering the operands leaves the triple product unchanged. This follows from the preceding property and the commutative property of the dot product: 𝐚⋅(𝐛×𝐜)... from wikipedia.org

5. Algebra(Abstract Noun) a polynomial of degree 2, meaning the highest exponent of the variable is two.