By: Sal Khan
Proving the triangle inequality for vectors in Rn Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.
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By: Sal Khan
Definitions of the vector dot product and vector length Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.
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By: Sal Khan
Proving the associative, distributive and commutative properties for vector dot products. Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.
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By: Sal Khan
Proof: Relationship between the cross product and sin of angle between vectors Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.
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By: Sal Khan
Proof of the Cauchy-Schwarz Inequality Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.
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By: Sal Khan
Distance between a point and a plane in three dimensions Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.
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By: Sal Khan
Figuring out a normal vector to a plane from its equation Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.
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By: Sal Khan
Dot and Cross Product Comparison/Intuition Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.
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By: Sal Khan
2010 IIT JEE Paper 1 Problem 51 Distance Between Planes Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.
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By: Sal Khan
Introducing the idea of an angle between two vectors Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.
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By: Sal Khan
Determining the equation for a plane in R3 using a point on the plane and a normal vector Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.
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By: Sal Khan
Introduction to the cross product Let's get our feet (and probably the rest of our body) wet in thinking in terms of vectors and spaces.
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By: Sal Khan
Variance as a measure of, on average, how far the data points in a population are from the population mean Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.
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By: Sal Khan
Review of what we've learned. Introduction to the standard deviation. Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.
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By: Sal Khan
Playing with the formula for variance of a population. Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.
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By: Sal Khan
Simulation by Peter Collingridge giving us a better understanding of why we divide by (n-1) when calculating the unbiased sample variance. Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.
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By: Sal Khan
Simulation by KA user tetef showing that dividing by (n-1) gives us an unbiased estimate of population variance. Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.
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By: Sal Khan
Thinking about how we can estimate the variance of a population by looking at the data in a sample. Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.
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By: Sal Khan
Reviewing the population mean, sample mean, population variance, sample variance and building an intuition for why we divide by n-1 for the unbiased sample variance Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.
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By: Sal Khan
Ben Eater and Sal Khan talk through the Khan Academy Standard Deviation 1 Module Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.
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