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why geometric multiplicity is bounded by algebraic multiplicity? 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
statistics - What are differences between Geometric, Logarithmic and . . . 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
When is a Power Series a Geometric Series? So surely you see the answer now, but I'll state it for the record: a power series is a geometric series if its coefficients are constant (i e all the same) In particular, not all power series are geometric For example $\sum x^n$ is geometric, but $\sum \frac {x^n} {n!}$ is not
terminology - Is it more accurate to use the term Geometric Growth or . . . 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?
Arithmetic or Geometric sequence? - Mathematics Stack Exchange 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 $\frac {\frac {1} {2}} {1}=\frac {1} {2}$
Calculate expectation of a geometric random variable 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
What is the difference between arithmetic and geometrical series? 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
What does the dot product of two vectors represent? 21 It might help to think of multiplication of real numbers in a more geometric fashion $2$ times $3$ is the length of the interval you get starting with an interval of length $3$ and then stretching the line by a factor of $2$ For dot product, in addition to this stretching idea, you need another geometric idea, namely projection