Polynomials of 2 Variables: General Form & Matrix Representation

  • Thread starter Thread starter complexhuman
  • Start date Start date
AI Thread Summary
The general form of a polynomial in two variables is expressed as a sum of terms involving both variables, such as a_0 x^n + a_1 x^{n-1} y + a_2 x^{n-2} y^2 + ... + a_n y^n, where P(x) and Q(y) represent polynomials in x and y, respectively. Each coefficient a_i corresponds to a specific term in the polynomial. To represent this polynomial using a matrix, one can organize the coefficients into a matrix format that reflects the degrees of x and y. This matrix representation aids in visualizing the relationships between the coefficients and the polynomial terms. Understanding both the general form and matrix representation is crucial for working with polynomials of two variables.
complexhuman
Messages
22
Reaction score
0
how does one look like?I mean what's the general form? e.g. for a 1 var poly...general form = a0+a1x+a2^2+...+anx^n

and how could I represent that by a matrix?


Thanks
 
Mathematics news on Phys.org
How about

a_0 x^n + a_1 x^{n-1} y + a_3 x^{n-2} y^2 + \cdot \cdot \cdot + a_n y^n + P(x) + Q(y)

where P and Q are polynomials in their respective arguments?
 
Last edited:
respective arguments?
 
Arguments - meaning P(x) is a polynomial in x and Q(y) is a polynomial in y.
 
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
Back
Top