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.
A trinomial is a polynomial. All trinomials are polynomials but the opposite is not true. a trinomial= three unlike terms. a polynomial= "many" unlike terms.
Evaluating a polynomial is finding the value of the polynomial for a given value of the variable, usually denoted by x. Solving a polynomial equation is finding the value of the variable, x, for which the polynomial equation is true.
It will be a cubic polynomial.
No. Matrix addition (or subtraction) is defined only for matrices of the same dimensions.
It means that you can do any of those operations, and again get a number from the set - in this case, a polynomial. Note that if you divide a polynomial by another polynomial, you will NOT always get a polynomial, so the set of polynomials is not closed under division.
Call your matrix A, the eigenvalues are defined as the numbers e for which a nonzero vector v exists such that Av = ev. This is equivalent to requiring (A-eI)v=0 to have a non zero solution v, where I is the identity matrix of the same dimensions as A. A matrix A-eI with this property is called singular and has a zero determinant. The determinant of A-eI is a polynomial in e, which has the eigenvalues of A as roots. Often setting this polynomial to zero and solving for e is the easiest way to compute the eigenvalues of A.
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.
4, the same as the degree of the polynomial.
A matrix having the same number of rows and columns is a SQUARE MATRIX.
A trinomial is a polynomial. All trinomials are polynomials but the opposite is not true. a trinomial= three unlike terms. a polynomial= "many" unlike terms.
yes
If a polynomial expression is derived from a word problem it has the same meaning as the word problem. Polynomial expressions that represent scientific laws have the specific meaning of that law.
No. A monomial (watch the spelling, please - only one "no") is a special case of a polynomial. A polynomial may have any number of terms; a monomial has exactly one term.
1.Sparse matrix representation 2. polynomial manipulation 3.dyanamic memory storage 4.in symbol table
A polynomial is a sum of a finite number of terms in which each term is of the form a*Xn where a is a coefficient, X is a variable and n is a non-negative integer.a may be integer, rations, real or complex;X may be a numerical variable or a matrix.
I suspect that the answer is a homogeneous polynomial.
For example, if you divide a polynomial of degree 2 by a polynomial of degree 1, you'll get a result of degree 1. Similarly, you can divide a polynomial of degree 4 by one of degree 2, a polynomial of degree 6 by one of degree 3, etc.