The geometric multiplicity is the number of linearly independent vectors, and each vector is the solution to one algebraic eigenvector equation, so there must be at least as much algebraic multiplicity.
Now lets do it using the geometric method that is repeated multiplication, in this case we start with x goes from 0 to 5 and our sequence goes like this: 1, 2, 2•2=4, 2•2•2=8, 2•2•2•2=16, 2•2•2•2•2=32. The conflicts have made me more confused about the concept of a dfference between Geometric and exponential growth.
For example, there is a Geometric Progression but no Exponential Progression article on Wikipedia, so perhaps the term Geometric is a bit more accurate, mathematically speaking? Why are there two terms for this type of growth? Perhaps exponential growth is more popular in common parlance, and geometric in mathematical circles?
2 A clever solution to find the expected value of a geometric r.v. is those employed in this video lecture of the MITx course "Introduction to Probability: Part 1 - The Fundamentals" (by the way, an extremely enjoyable course) and based on (a) the memoryless property of the geometric r.v. and (b) the total expectation theorem.
A geometric sequence is one that has a common ratio between its elements. For example, the ratio between the first and the second term in the harmonic sequence is $\frac {\frac {1} {2}} {1}=\frac {1} {2}$.
Geometric and arithmetic are two names that are given to different sequences that follow a rather strict pattern for how one term follows from the one before. An arithmetic sequence is characterised by the fact that every term is equal to the term before plus some fixed constant, called the difference of the sequence. For instance, $$ 1,4,7,10,13,\ldots $$ is an arithmetic sequence with ...
The geometric multiplicity is the dimension of the eigenspace of each eigenvalue and the algebraic multiplicity is the number of times the eigenvalue appears in the factorization of the caracteristic polynomial.
A geometric sequence has its first term equal to $12$ and its fourth term equal to $-96$. How do I find the common ratio? And find the sum of the first $14$ terms
