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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
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What is the definition of a null matrix?
The null matrix is also called the zero matrix. It is a matrix with 0 in all its entries.
What da hell is inverse proportion?
Inverse proportion is a mathematical concept and has nothing whatsoever to do with religious concepts such as hell.
What is a magnetic field vector?
It is a way of representing the magnetic force at a point in the field. The magnitude and direction of the vector represents the strength and the direction of the magnetic force acting on a charged particle in the field.
When can you not invert a matrix?
If it is not a square matrix.
You cannot invert a square matrix if it is singular. That means that at least one of the rows of the matrix can be expressed as a linear combination of the other rows.
A simple test is that a matrix cannot be inverted if its determinant is zero.
What are the relation that is also a function?
A relation is a mapping between elements of two sets - which need not be different sets. The relationship may be one-to-one or many-to-one but not one-to-many. In graphical form, any line which is parallel to the y-axis can meet the plot at most once.
This site no longer allows me to enter subscripts so I will use brackets: a(n) to indicate the nth term.
a(n) = a(1) + (n-1)*d where d is the common difference between the terms of the arithmetic sequence.
Therefore, d = [a(n) - a(1)]/(n-1)
Then, the appropriate arithmetic series is
S(n) = 1/2*n[2*a(1) + (n-1)*d] where all the terms on the right hand side are known.
How an algebric expression with quadratic denominator is solved?
Algebraic expressions can't be solved because they are not equations but they can be simplified.
What is finite and infinite cyclic group?
Normally, a cyclic group is defined as a set of numbers generated by repeated use of an operator on a single element which is called the generator and is denoted by g.
If the operation is multiplicative then the elements are g0, g1, g2, ...
Such a group may be finite or infinite. If for some integer k, gk = g0 then the cyclic group is finite, of order k. If there is no such k, then it is infinite - and is isomorphic to Z(integers) with the operation being addition.
The equation is x = -7.
What fractions are between one fourth and one third?
fraction between 1/4 and 1/3 is 7/24 or 13/48, 14/48, 15/48one fourth = 1/4 but 1/4 is also equal to 3/12 or 6/24 or 12/48one third = 1/3 but 1/3 is also equal to 4/12 or 8/24 or 16/48
thus, fraction between 1/4 and 1/3 is 7/24 or 13/48, 14/48, 15/48
How can you tell if a matrix is invertible?
An easy exclusion criterion is a matrix that is not nxn. Only a square matrices are invertible (have an inverse). For the matrix to be invertible, the vectors (as columns) must be linearly independent. In other words, you have to check that for an nxn matrix given by {v1 v2 v3 ••• vn} with n vectors with n components, there are not constants (a, b, c, etc) not all zero such that av1 + bv2 + cv3 + ••• + kvn = 0 (meaning only the trivial solution of a=b=c=k=0 works).
So all you're doing is making sure that the vectors of your matrix are linearly independent. The matrix is invertible if and only if the vectors are linearly independent. Making sure the only solution is the trivial case can be quite involved, and you don't want to do this for large matrices. Therefore, an alternative method is to just make sure the determinant is not 0. Remember that the vectors of a matrix "A" are linearly independent if and only if detA�0, and by the same token, a matrix "A" is invertible if and only if detA�0.
Is matrix polynomial and polynomial matrix same?
No.
A matrix polynomial is an algebraic expression in which the variable is a matrix.
A polynomial matrix is a matrix in which each element is a polynomial.
