More about Equations
... Given that the simultaneous equations have only one solution, find the value of k. y = −10 x ...
... Given that the simultaneous equations have only one solution, find the value of k. y = −10 x ...
noncommutative polynomials nonnegative on a variety intersect a
... proofs, chip spaces. Also we state our main theorems in terms of chip spaces since keeping track of the chip space where each polynomial lies adds significant generality, and leads to optimal degree and size bounds; cf. [KP10]. Consider R1×` hx, x∗ i. A monomial ei ⊗ a divides another monomial ej ⊗ ...
... proofs, chip spaces. Also we state our main theorems in terms of chip spaces since keeping track of the chip space where each polynomial lies adds significant generality, and leads to optimal degree and size bounds; cf. [KP10]. Consider R1×` hx, x∗ i. A monomial ei ⊗ a divides another monomial ej ⊗ ...
Like terms
... The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms. ...
... The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms. ...
Linear algebra
Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.The set of points with coordinates that satisfy a linear equation forms a hyperplane in an n-dimensional space. The conditions under which a set of n hyperplanes intersect in a single point is an important focus of study in linear algebra. Such an investigation is initially motivated by a system of linear equations containing several unknowns. Such equations are naturally represented using the formalism of matrices and vectors.Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations.Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, computer animation, and the social sciences (particularly in economics). Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear models.