Equations, formulae and identities
... identity, identically equal, inequality… subject of the formula… common factor, factorise… index law… linear, quadratic, cubic… and the identity sign (≡). ...
... identity, identically equal, inequality… subject of the formula… common factor, factorise… index law… linear, quadratic, cubic… and the identity sign (≡). ...
Math 215 HW #9 Solutions
... Turning to the checkerboard matrix C, notice that the first two columns are linearly independent, but that the third and fourth columns are repeats of the first two columns, so the matrix must have rank 2. Therefore, one eigenvalue is 0; the corresponding eigenvectors will be the elements of the nul ...
... Turning to the checkerboard matrix C, notice that the first two columns are linearly independent, but that the third and fourth columns are repeats of the first two columns, so the matrix must have rank 2. Therefore, one eigenvalue is 0; the corresponding eigenvectors will be the elements of the nul ...
Boolean algebra
... Given a truth table for a Boolean function, construction of the product-of-sums representation is trivial: - for each row in which the function value is 0, form a product term involving all the variables, taking the variable if its value is 1 and the complement if the variable's value is 0 - take th ...
... Given a truth table for a Boolean function, construction of the product-of-sums representation is trivial: - for each row in which the function value is 0, form a product term involving all the variables, taking the variable if its value is 1 and the complement if the variable's value is 0 - take th ...
Course of analytical geometry
... the analytical geometry in this book is a geometry of threedimensional space E. We use the symbol E for to denote the space that we observe in our everyday life. Despite being seemingly simple, even the empty space E possesses a rich variety of properties. These properties reveal through the propert ...
... the analytical geometry in this book is a geometry of threedimensional space E. We use the symbol E for to denote the space that we observe in our everyday life. Despite being seemingly simple, even the empty space E possesses a rich variety of properties. These properties reveal through the propert ...
THE COTANGENT STACK 1. Introduction 1.1. Let us fix our
... schemes) we have an isomorphism βf : f ∗ FU0 −→ FU such that these isomorphisms satisfy the cocycle condition that βf ◦ f ∗ (βf 0 ) = βf 0 ◦f whenever we have morphisms f ...
... schemes) we have an isomorphism βf : f ∗ FU0 −→ FU such that these isomorphisms satisfy the cocycle condition that βf ◦ f ∗ (βf 0 ) = βf 0 ◦f whenever we have morphisms f ...
On the Solution of Linear Algebraic Equations Involving Interval Coe
... arithmetic, since the support set of this arithmetic is the set of both proper and improper intervals, which we call directed intervals 9]{10]. Directed interval arithmetic is the natural arithmetic for the solution of algebraic equations, since it is obtained from the arithmetic for normal interv ...
... arithmetic, since the support set of this arithmetic is the set of both proper and improper intervals, which we call directed intervals 9]{10]. Directed interval arithmetic is the natural arithmetic for the solution of algebraic equations, since it is obtained from the arithmetic for normal interv ...
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.