Tagged Questions
5
votes
2answers
67 views
Why the SVD is named so…
The SVD stands for Singular Value Decomposition. After decomposing a data matrix X using SVD, it results three matrices, two singular vactors U and V, and one singular value matrix whose diagonal ...
-4
votes
2answers
118 views
Why cross product's formulas defined in this way?
Why cross product's formulas defined in this way?
When mathematicians need to define cross product?
2
votes
2answers
112 views
Why is the Leibniz formula for determinants called such?
My professor said that Leibniz was not even aware of the concept. The Wikipedia page says that the formula was named "in honor of Gottfried Leibniz." What gives? Did he do work that was related, and ...
16
votes
3answers
567 views
Why, historically, do we multiply matrices as we do?
Multiplication of matrices — taking the dot product of the $i$th row of the first matrix and the $j$th column of the second to yield the $ij$th entry of the product — is not a very ...
1
vote
1answer
236 views
Why are vector spaces sometimes called linear spaces?
I have never come across the term 'linear space' as a synonym for 'vector space' and it seems from the book I am using (Linear Algebra by Kostrikin and Manin) that the term linear space is more ...
10
votes
1answer
277 views
Who was the first to use dual space?
Who was the first person who used the dual space? In which paper / book did he or she use the dual space?
Who was the first who called it dual space and in which paper / book?
5
votes
4answers
305 views
The contributions of James Sylvester to linear algebra.
The claim is James Sylvester and Arthur Cayley are the fathers of Linear Algebra. I can find the various parts that Cayley contributed to Linear Algebra, but there is not much on the contributions ...
3
votes
1answer
307 views
References on the History of Linear Algebra
I have an aggregated understanding of the history of linear algebra compiled from friends, teachers, and coworkers. It may have several errors. It goes something like this:
Even ancient cultures ...
0
votes
1answer
338 views
History of solving linear equations with matrices
I'm solving linear equations with matrices right now and I wonder, how did it start.
Who, how, why came to idea that such kind of equations could be solved with matrices? What was first: matrix or ...
12
votes
4answers
1k views
Origin of the dot and cross product?
Most questions usually just relate to what these can be used for, that's fairly obvious to me since I've been programming 3D games/simulations for a while, but I've never really understood the inner ...
6
votes
2answers
258 views
What's the “geometry” in “geometric multiplicity”?
The geometric multiplicity of an eigenvalue is defined as the dimension of the associated eigenspace, i.e. number of linearly independent eigenvectors with that eigenvalue.
Here are my questions:
...
10
votes
2answers
904 views
History of dot product and cosine
The fact that the dot product and the cosine of the angle between two vectors are mutually computable is easy to show (see the two sides in the two answers at Dot product in coordinates).
But looking ...
2
votes
1answer
679 views
What does matrix multiplication have to do with scalar multiplication?
Why are matrix and scalar multiplication denoted the same way and treated as the same operation in standard mathematical notation? This is always a source of confusion for me because they have ...
2
votes
3answers
986 views
What is Modern Mathematics? Is this an exact concept with a clear meaning? [closed]
Motivated by this question I would like to know whether there is an exact definition of modern mathematics. In which point in time (century, decade) does one think, when speaking about modern ...
