The covariance matrix

CORRECTION: At 10:56 we shouldn't divide by 4 to get the covariance, we should divide by 1+1+1+1/3, which is 10/3. That means the covariances are the following:
Var(x) = 1.056
Var(y) = 0.864
Cov(x,y) = 0.768
(Thank you Shivkumar Pippal!)

Mean, variance, covariance, and the covariance matrix for a dataset and a weighted dataset.

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0:00 Introduction
0:09 The covariance matrix
2:22 Average
3:23 X-variance
5:06 Problem: Same variances
7:59 Formulas
10:30 Center points

[hansenmarc]

When I remember that var(x) is the same as cov(x, x), the formulas in the covariance matrix seem more consistent and make more sense to me. In other words, the whole matrix can also be defined in terms of covariances alone.

[cocoarecords]

seriously one of the best and most intuitive channels on this subject. I can show your videos to my child and he will understand

[shubhamtalks]

While I know covariance matrix, It is always interesting to learn concepts from your perspective.

[blesucation]

Just want to leave a comment so that more people could learn from your amazing videos! Many thanks for the wonderful and fun creation!!!

[atinsood]

thank you for this, there were so many hidden tidbits of knowledge in this. thank you for making these and appreciate the attention in explaining small details.

[deepthik]

You know the way how people understand. Keep posting videos. These are much elaborated.

[YanivGorali]

After watching many videos on the subject, this one finally helped me understand. Thank you

[prikas]

Extremely helpful and easy to understand as someone new to this topic. Thank you for your work and actually showing examples with numbers for how each part in the covariance matrix was calculated.

[moudjarikhadidja]

Great video, very intuitive Thanks a lot.
At 12:25 in the variance formula, we divide by the sum of all weights and not the sum of weights squared and it is the same for the covariance, right?

[shivkumarpippal]

at 10:56, shouldn't it be divided by 10/3 instead of 4 as we've 3 and one third data points?

[mikhailgritskikh]

In my opinion it would be useful to see connection between the covariance matrix and matrix transformations. Could you make a video on that please?

[luccaemmanuel]

this video deserves more views. Incredible work, thank you.

[blakete]

Fantastic video. Made the covariance very intuitive. Thank you!

[abhisheksolanki]

best explanation of covariance on youtube

[wsylovezx]

Thank you for this great video. A bit inconsistency between the correction 1/3 (under ur comments) and the formula alpha^2 (at 12:24). I think the formula is correct and in the concrete example 1/3 should changed to be 1/9.

[ricardoraymond]

This guy has a gift to make the tough look easy!

[ff-ym]

Hi, in 11:23, why are you not subtracting the values by mean before squaring them? the formulae you showed earlier shows subtracting by mean

[simonpinnock]

Very clearly explained, well done and many thanks!

[nettwrrk]

thanks dude, couldn't understand any explanation of all that before i found your video

[ArduinoHocam]

This is a great visualization and a perspective that should everyone need to know. To see what is the magic behind the scene, visualization is best way as always...