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Abstract Algebra
Have you ever wondered what would happen if you redefined some of the basic rules of algebra so that concepts you took for granted, like AB = BA, no longer apply? Abstract algebra does just that through the study of the properties that define algebraic structures. Post all questions about fields, rings, group theory, vector spaces, and the axioms that define them into this category.
1,849 Questions
His pants fit him like a glove.
There are two types of mathematical axioms: logical and non-logical.
Logical axioms are the "self-evident," unprovable, mathematical statements which are held to be universally true across all disciplines of math. The axiomatic system known as ZFC has great examples of logical axioms. I added a related link about ZFC if you'd like to learn more.
Non-logical axioms, on the other hand, are the axioms that are specific to a particular branch of mathematics, like arithmetic, propositional calculus, and group theory. I added links to those as well.
What number combinations equal 50?
Lots of combinations equal 50, here are a few.... 1+49, 2+48, 3+47, 4+46 and so on 2x25, 5x10, 10x5 etc. 300/6, 1200/24, 12+8=20+30 or.. 3x10=30+20, 3x14=42+8, 6x8=48+2 ..... we could be here a long time, you get the idea!
What is the formula of bordered Hessian matrix?
The bordered hessian matrix is used for fulfilling the second-order conditions for a maximum/minimum of a function of real variables subject to a constraint. The first row and first column of the bordered hessian correspond to the derivatives of the constraint whereas the other entries correspond to the second and cross partial derivatives of the real-valued function. Other than the bordered entries, the main diagonal of the sub matrix consists of entries for the second partial derivatives. All other entries of the sub matrix off of the main diagonal correspond to all combinations of cross partials. Evaluating the determinant of the bordered hessian will allow one to determine if the function attains its maximum or minimum at the stationary points, which by the way are limited in the fact that they must both satisfy the gradient equations and the constraint.
An idempotent matrix is a matrix which gives the same matrix if we multiply with the same.
in simple words,square of the matrix is equal to the same matrix.
if M is our matrix,then
MM=M.
then M is a idempotent matrix.
Are computers based on boolean algebra?
Very deep in the computer, yes. The 3rd+ level programming languages, no.
Is every finite abelian group is cyclic?
No, for instance the Klein group is finite and abelian but not cyclic. Even more groups can be found having this chariacteristic for instance Z9 x Z9 is abelian but not cyclic
What is the value of a 1712 coin?
The value of a 1712 coin would vary widely. It would depend on its denomination, country of origin, and condition. It could be worth thousands of dollars if collectible enough.
What are 3 types of variables?
There are many ways of categorising variables. One classification, used in statistics, is Nominal, Ordinal and Interval.
We use algebra for many reasons and one of them is for replacing knowm values into unknown values
63072000 seconds for a regular year, but 63244800 seconds in a leap year.
engineers, every single teacher, chemists, laboratory technicians
What is the value of a 1968 pfennig?
Many of the coins are valued in price close to $4 each. The amount for each will depend upon the condition that it is in.
Matrices are used in most scientific fields. They are usually used to represent and manipulate a number of measures simultaneously.
For example, they are used to represent and solve systems of simultaneous equations. In basic mechanics could represent the coordinates of the location of particles or specific locations on a rigid body. Joint probability distributions - for n variables - are represented, using matrices, as surfaces in n+1 dimensional space.
the order is m p and the matrices can be multiplied if and only if the first one (matrix A) has the same number of columns as the second one (matrix B) has rows i.e)is Matrix A has n columns, then Matrix B MUST have n rows.
Equal Matrix: Two matrices A=|Aij| and B=|Bij| are said to be equal (A=B) if and only if they have the same order and each elements of one is equal to the corresponding elements of the other. Such as A=|1 2 3|, B=|1 2 3|. Thus two matrices are equal if and only if one is a duplicate of the other.
Group formed by political body in order to communicate with groups outside of the colony?
Are you in Parzych's class? Anyway, the answer is 'A committee of correspondence.' ~Billy
Algebra was my favorite subject and I have found none of its uses helpful to me, but a few of the uses are to find the distance of a bus and when you will arrive by doing the formula D=RxT distance equals rate times time. and finding when the two buses would arrive if they left at the same time if they were going different speeds or if they left at different times going the same speed by using another formula. There are many little things like that that it can be used for, none of which I would exert my time and energy to find out. but you could definitely use algebra for something in life.
-- Amanda
