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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

What is the definition of payroll?

The payroll is the amount of money a company/business/establishment pays its employees at any given time -- sometimes every two weeks, or sometimes once every month. For more information, see the Related Link.

What is an example of a matrix?

The Matrix is everywhere. It is all around us. Even now, in this very room. You can see it when you look out your window or when you turn on your television. You can feel it when you go to work... when you go to church... when you pay your taxes. It is the world that has been pulled over your eyes to blind you from the truth.

But seriously- { { 2 5 7 }

{ 3 0 0 }

{ 2 9 2 } }

It is usually written with one pair of large brackets, like this:

/ 2 5 7 \

< 3 0 0 >

\ 2 9 2 /

What is the definition of a symmetric matrix?

Symmetric Matrix:

Given a square matrix A such that A'=A, where A' is the transpose of A, then A is a symmetric matrix.

note: No need to think about diagonal elements, they can be anything.

What fraction is between one fourth and one fifth?

One way to get a number between two numbers - specifically, the number that is exactly in the middle between both - is to take the average of the two numbers. Just add the two numbers, and divide the result by 2.

What is the value of an 1832 dime?

You have a rare Capped Bust Dime - if it is in good condition (G$), its value is: $35.00.

What is the value of a 1938 dime?

10 cents

More:This 1938 Mercury Dime is made out of silver so as of 10/2010, the value of silver content is about $1.70 ($24.30 per ounce of silver). The numismatic value of the coin depends on where it was minted and what condition the coin is in. It was minted in Philadelphia, Denver and San Francisco. According to USA Coin Book, these are the values:

Philadelphia (no mint mark): In Good condition, this coin is worth about $1.80 up to about $15 in MS60 mint condition. In MS65 brilliant uncirculated condition, this coin is worth roughly $30. Proof coins were also minted here and are worth about $525.

Denver (small "D" mint mark): In Good condition, this coin is worth about $1.95 up to about $25 in MS60 mint condition. In MS65 brilliant uncirculated condition, this coin is worth roughly $35.

San Francisco (small "S" mint mark): In Good condition, this coin is worth about $1.80 up to about $28 in MS60 mint condition. In MS65 brilliant uncirculated condition, this coin is worth roughly $38.

How matrices used in engineering?

If you have a system, which can be expressed as a set of linear equations, then you can utilize matrices to help solve it. One example is an electrical circuit which uses linear devices (example are constant voltage sources and resistive loads). To find the current through each device, a set of linear equations is derived.

Is the moon orbit an example of a parabola?

No. Every closed orbit (around and around and around) is an ellipse.

Every open orbit (swish by one time and never return) is a hyperbola.

The one that's exactly precisely on the dividing line between closed and

open is a parabola.

How do you translate a word problem into a mathematical sentice?

To translate a word problem into a mathematical sentence, first identify the key elements such as quantities, relationships, and operations involved. Assign variables to unknowns and translate phrases into mathematical symbols, like using "+" for "more than" or "=" for "is." Organize the information logically, ensuring that the equation reflects the relationships described in the problem. Finally, review the sentence to ensure it accurately represents the original scenario.

How do you inverse complex matrix with Armadillo linear algebra library?

To invert a complex matrix using the Armadillo linear algebra library, you can utilize the inv() function, which computes the inverse of a matrix. First, ensure you include the Armadillo header and link against the library. Here's a simple example:

#include <armadillo>

arma::cx_mat A = {{1.0, 2.0}, {3.0, 4.0}}; // Define a complex matrix
arma::cx_mat A_inv = inv(A); // Invert the matrix

Make sure the matrix is square and non-singular for the inversion to be valid.

How is a vector represented in a diagram?

It is usually represented by a lower case letter with a horizontal arrow above it. In print, the letter will usually be bold.

What is the value of mossberg 185d?

as of 2007 a mossberg 185d in excellent condition will retail for approximately $90. This specific model is a bolt action 20 gauge shotgun with a 2 round removable magazine and screw on choke tubes. They were manufactured from 1947 until 1950.

How is the strength of an electric field indicated with electric field lines?

Given a positive charge the electric field lines are drawn starting from the charge and pointing radially outward, ending in principle at infinity, according to the electric field strength being proportional to the inverse square of distance. From the definition of electric field we know that the modulous of the electric field is greater for smaller distances from the field generating charge. Since the electric field lines point radially outward we consider the density of lines an indication of the strength of the electirc field. If we immagine to trace a circle around the electric field generating charge, of radius slightly greater than the radius of the object which holds the charge and therefore generates the electric field, such circle will be crossed by a number 'n' of lines. The density of lines crossing the cirle will then be the circumference of the circle divided by the number 'n' of lines. For a larger circle we will have a greater circumference, but same number of lines 'n', and therefore a smaller density of lines crossing it, which idicates a lower intesity of electric field for a greater distance from the charge.

What is the value of a 1998 Ford Escort?

Depends on many factors. Your location, how the car is equipped, mileage, and most important, condition of the vehicle. Go to:

www.nada.com to find the value.

www.kbb.com or www.kellybluebook.com is a great way to figure it out as well.

On that note, surprisingly I recently priced out a 1998 ford escort with around 125 thousand miles on it, and in excellent condition the car is worth roughly $2,800(according to www.kbb.com)

How does someone make a first in math account?

You need approval from a teacher and have them make you an account, but it only lasts for 1 year unless you renew it.

Value of a lorcin 380?

It's a poorly manufactured gun that is prone the failure and breakage. If you are the potential buyer, just keep looking. If you are the potential seller, turning it in on when the police department is running a buyback program would net you more than you could sell it for. Value is no more than $50.