Abstract The initial value problem for a matrix Riccati differential equation associated with an M-matrix is known to have a global solution X(t) on [0, ∞) when X(0) takes values from a suitable set ...

This is a preview. Log in through your library . Consists of six departments and provides education in the fields of physics, mathematics, chemistry, informatics, biology and ecology, geography and ...

Now, we know that I3 = I1 + I2, so V IN must be a nice linear function of V OUT and I1, namely: where F1 and F2 are functions of R1, R2, C1, and C2—and of frequency. We derived that equation just by ...

If \(A\) is a \(3\times 3\) matrix then we can apply a linear transformation to each rgb vector via matrix multiplication, where \([r,g,b]\) are the original values ...

Most linear algebra courses start by considering how to solve a system of linear equations. \[ \begin{align} a_{0,0}x_0 + a_{0,1}x_0 + \cdots a_{0,n-1}x_0 & = b_0 ...

A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations. Polynomials are equations involving a variable raised to powers, such ...

You guys may have noticed that recently, I have been showing you a lot of algebraic equations. I really don't like to use, or generate, algebraic equations. Sometimes they're much messier than just ...