Vector space is an important subject in modern mathematics. Therefore, linear algebra is widely used in abstract algebra and functional analysis. Linear algebra can be expressed concretely by analytic geometry. The theory of linear algebra has been generalized to operator theory. Since nonlinear models...
Many studies provide insights into students' conceptions of various linear algebra topics and difficulties they face with multiple modes of thinking needed... G Karakok - 《Zdm the International Journal on Mathematics Education》 被引量: 0发表: 2019年 What Is Calculus?: From Simple Algebra To De...
This question shows research effort; it is useful and clear 3 Save this question. Show activity on this post. This question is motivated by the following problem from a problem set on ring theory: Prove that, if RR is a Noetherian commutative ring, and II is its...
An interesting answer is provided by exterior algebra. It may not be what you expect if you're unfamiliar with the subject, but it can give you some geometric intuition if you accept that linear operators can also naturally act onvolumesin the space they're defined. ...
this, we have different branches of mathematics, and we can further classify those branches based on specific topics within each branch. Algebra is one branch that has evolved through the years; two types of algebra into which its history can be divided are modern algebra and classical algebra....
is a linear combination if are real numbers. A concrete example is the following: a basis for the x-y plane is the vectors . Any vector is of the form which can be written as so we indeed have a basis! This is not the only possible basis. In fact, the vectors in our basis don...
It helps in transforming real-life problems into an algebraic expression in mathematics. Forming a mathematical expression of the given problem statement is part of pre-algebra.Elementary AlgebraElementary algebra deals with solving the algebraic expressions for a viable answer. In elementary algebra, ...
Discrete mathematics and probability Abstract Algebra Abstract algebra is one of the divisions in algebra which discovers the truths relating to algebraic systems independent of the specific nature of some operations. These operations, in specific cases, have certain properties. Thus we can conclude some...
In real life, linear programming is part of a very important area of mathematics called "optimization techniques". This field of study (or at least the applied results of it) are used every day in the organization and allocation of resources. These real life systems can have dozens of variab...
be further broken into basic concepts known as elementary algebra or the more abstract study of numbers and equations known as abstract algebra, where the former is used in most mathematics, science, economics, medicine, and engineering while the latter is mostly used only in advanced mathematics....