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ChiralSuperfields
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Dose someone please know why they have the absolute value bars in this derivation?
many thanks!
many thanks!
Thank you for your help @jedishrfu !jedishrfu said:
The absolute value bars in dot product derivation are used to ensure that the resulting value is always positive. This is important because the dot product is a measure of the similarity or correlation between two vectors, and a negative value would indicate a negative correlation.
In the dot product formula, the absolute value bars are used to enclose the values of the two vectors being multiplied together. This ensures that the resulting value is always positive, regardless of the signs of the individual components of the vectors.
No, the absolute value bars cannot be removed from the dot product formula. Doing so would change the meaning of the formula and could result in incorrect calculations.
The dot product can be thought of as the absolute value of the projection of one vector onto another because it measures the length of the projection of one vector onto another, regardless of the angle between the two vectors.
Yes, there are alternative ways to represent the dot product without using absolute value bars. For example, the dot product can also be calculated using the cosine of the angle between the two vectors multiplied by the magnitudes of the vectors. However, using absolute value bars is the most commonly used and accepted method for calculating the dot product.