Negative Indices: Explaining the "Super Minus

In summary, the conversation is about a person struggling to understand the concept of "super minus" in a paper about the Kalman Filter. They have asked their teachers for clarification but have not received a satisfactory answer. Another person suggests that the notation is used to distinguish between "a priori" and "a posteriori" measurements, but they are not familiar with the paper and suggest waiting for someone who is to confirm or contradict their interpretation.
  • #1
Gepard
18
0
Hi,

Apologies if this is in the wrong place but I've no idea what *it* does...

I should just mention that I'm currently doing my A-levels (16) and so my maths skills aren't that advanced...

The problem:
I've found a paper on the Kalman Filter on the internet (source: http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf)

Now, I'm trying to get my head around it, but am struggling with what the "'super minus'" means at the bottom of page 2.

I've asked all the teachers at school and none of them have any idea and keep telling me it's a typo and we've only dealt with indices that have a number in them.

Could someone here please explain what it means?

Cheers,

Michael
 
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  • #2
Well, firstly, I don't know anything about the topic, but it is clearly not a typo! My take on it is that it just a notation: he is using the superscript - to distinguish the "a priori" measurements from the "a posteriori" measurements (with no superscript). In this sense the superscript - doesn't itself "mean" anything-- he could have used a ' or anything else to distinguish this, but just chose the -

Hope that helps, but you may have to wait for someone who is familiar with the paper to confirm (or contradict) what I have just said!
 
  • #3
Thanks Cristo, that makes a lot of sense.

Cheers,

Michael
 

What are negative indices and how are they used in mathematics?

Negative indices are a way of representing numbers or variables in the form of fractions or powers. They are used to indicate the reciprocal of a number or the inverse of a power. For example, x-2 is the same as 1/x2, and 2-3 is the same as 1/23.

Why are negative indices sometimes referred to as "super minus"?

Negative indices are sometimes called "super minus" because they are written as a superscript (above the normal line of text) and have the same effect as a minus sign. This notation is used to differentiate them from positive indices, which are written as a normal number or variable.

What happens when a negative index is applied to a number or variable?

When a negative index is applied to a number or variable, it indicates that the number or variable is being raised to a negative power. This means that the number or variable is being divided by itself multiple times, depending on the value of the negative index. For example, x-3 is the same as 1/x3, which means that x is being divided by itself three times.

In what situations would negative indices be used?

Negative indices are commonly used in algebra, calculus, and other branches of mathematics. They are especially useful in simplifying expressions and solving equations involving powers and fractions. Negative indices can also be used to represent numbers or variables in certain scientific and engineering equations, such as those involving electrical resistance and radioactive decay.

Are there any rules or properties that apply to negative indices?

Yes, there are several rules and properties that apply to negative indices, including the product rule, quotient rule, and power rule. These rules state that when multiplying or dividing numbers or variables with negative indices, the indices can be added or subtracted respectively. Additionally, when raising a number or variable with a negative index to a power, the indices can be multiplied. These rules can help simplify expressions and solve equations involving negative indices.

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