In linear algebra, the main diagonal of a square matrix is the diagonal which runs from the top left corner to the bottom right corner. For example, the following matrix has 1s down its main diagonal: Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations. ... For the square matrix section, see square matrix. ...
A matrix like the above in which only the elements of the main diagonal are non-zero is called a diagonal matrix. The sum of the entries on the main diagonal of a matrix is known as the trace of that matrix. In linear algebra, a diagonal matrix is a square matrix in which only the entries in the main diagonal are non-zero. ... In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i. ...
In engineering a diagonal brace is a beam used to cross brace a rectangular structure such as scaffolding to withstand sheer forces pusing into a rhombus; although called diagonal, due to practical considerations in practice diagonal braces are often not connected to the corners of the rectangle.
Diagonal pliers are wire-cutting pliers defined by the cutting edges of the jaws intersects the joint rivet at an angle or "on a diagonal", hence the name.
In general, the intersection number of the graph of a function with the diagonal may be computed using homology via the Lefschetz fixed point theorem; the self-intersection of the diagonal is the special case of the identity function.
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