# Questions tagged [linear-algebra]

For questions about linear algebra, a mathematical field studying vector spaces and matrices.

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### What was the role of Schmidt in derivation of the Gram-Schmidt process?

When reading the section related to Gram-Schmidt process in the book Linear Algebra and Its Applications by Gilbert Strang, I found a foot note that says: If Gram thought of it first, what was left ...
54 views

### Negative coefficients in the barycentric calculus

The barycentric calculus of Möbius involves formal sums of expressions of the form $mP$ where $m$ is a real number and $P$ is a point, where $mP$ is to be thought of as $m$ units of mass located at $P$...
43 views

### Understanding Grassmann's Approach to Algebras over Vector Spaces?

According to Hermann Grassmann and the creation of linear algebra by Desmond Sander, Grassmann was able to identify all the important notions in linear algebra in his book "Ausdehnungslehre"....
229 views

### Earliest mention of permutation matrices, or equivalent? More generally, matrices for arbitrary functions between finite sets?

Permutation matrices I assume have a long history, and would be surprised if they were first considered only long after the work of Shur just after 1900, on the representation theory of $S_n$. ...
80 views

### Sylvester's Quote on Determinants

What does the following quote by Sylvester mean? "A general algebraical determinant in its developed form may be likened to a mixture of liquids seemingly homogeneous, but which, being of ...
93 views

### Where does the "operator to the right" notation originate?

If any of you have ever written code in DirectX, you're sure to have noticed that applying a linear operator $A$ to a vector $x$ is done as $xA$, instead of the (nowadays usual) $Ax$. I wanted to know ...
141 views

### Why did Clifford Algebra suddenly gain a resurgence under the name of Geometric Algebra in recent years?

To my understanding, this new Geometric algebra thing is actually nothing more than years old Clifford Algebra. Yet it is advertised by many of its proponents as a fundamentally new thing; why is that?...
152 views

### How and by whom was the concept of generalized eigenvectors developed?

In general, a linear operator on a complex vector space need not always have an eigenspace decomposition. But it will always have enough generalized eigenvectors to provide a decomposition of the ...
88 views

### Who discovered the real Jordan form?

The real Jordan form is here. I want to know who discovered this form. I searched google academics for a long time but couldn't get an answer.