Comments on: What are eigenvectors and eigenvalues?

By: zh

zh — Fri, 21 Jul 2017 05:50:18 +0000

Great work

By: Swee Mok

Swee Mok — Tue, 06 Jun 2017 12:40:45 +0000

Great explanation.

It looks like there is a typo in the 2nd line while deriving equation (6). The lambda square should have a positive sign.

By: arun

arun — Sat, 01 Oct 2016 14:30:32 +0000

plz can u descibe its use in one application

By: Mayuri Sandhanshiv

Mayuri Sandhanshiv — Tue, 27 Sep 2016 06:26:47 +0000

Nice article. But I guess there is error in calculating second eigen vector. It should 2 3 instead of 3 2. Please check at your end and let us know. Thanks in advance !! I must say it is a very well written article.

By: Kaleo Brandt

Kaleo Brandt — Fri, 03 Jun 2016 05:53:15 +0000

I was also confused about this. After researching for a good hour or two on determinants and invertible matrices, I think it’s safe to say that a non-invertible matrix either:
– Has a row (or column) with all zeros
– Has at least two rows (or columns) that are equivalent.

The underlying reason for this (and its correlation with determinants) is that the determinant of a matrix is essentially the area in R^n space of the columns of the matrix (see http://math.stackexchange.com/questions/668/whats-an-intuitive-way-to-think-about-the-determinant).
So, if two of the columns of the matrix are equivalent, that means that they’re parallel, and the area of the parallelepiped formed has an area of zero. (It would also have an area of zero if one of the vectors is a null-vector).

So I think the reason is that, unless v is the null-vector of all zeros, one of the above properties is necessary for a linear combination of the rows to add up to zero (This is the part I’m unsure about, because the dimensions of equation (2) isn’t 1×1, is it?).

If someone actually knows what they’re talking about, please correct me. This is just my understanding after googling some stuff.

By: rahib ullah mullagori

rahib ullah mullagori — Tue, 08 Dec 2015 13:02:03 +0000

thanks and so great

By: Nrupatunga

Nrupatunga — Wed, 02 Dec 2015 08:47:07 +0000

Thank you Mr Vincent, I as well thought this is what you meant. Hope that wasn’t silly to ask.
Thank you for making it clear to me that its just mathematical manipulations.

Your blog is very neatly maintained. I would be very happy to learn more from you through your articles.

Thank you

By: Vincent Spruyt

Vincent Spruyt — Wed, 02 Dec 2015 07:36:59 +0000

Hi Nrupatunga,
Usually, we normalize the eigenvector such that its magnitude is one. In this case, the eigenvector only represents a direction, whereas its corresponding eigenvalue represents its magnitude.

By: Nrupatunga

Nrupatunga — Wed, 02 Dec 2015 07:17:16 +0000

Hi Vincent,
Thank you for writing such nice articles.

I have a question for you. In the post you have written that ” Since an eigenvector simply represents an orientation”.
When you say something as a “Vector” it means that it has both direction and magnitude. But this statement was confusing for me.
Can you please explain what do you mean by this statement?

Thank you
Nrupatunga

By: Brain, Song

Brain, Song — Mon, 30 Nov 2015 07:26:50 +0000

Another Trivial Thing: I think x22 = 2/3 x21 on [13]
Thanks for your explicit explanation.