Matrices

# Square matrices

The (main) **diagonal** of a square matrix is formed by the elements a_{11}, a_{22}, …,a_{nn}. The **trace** is the addition of these elements:

Example:

The **identity or unit matrix** is:

and it verifies that it is the identity element of multiplication, that is:

A square matrix is said to be **symmetric** if *A ^{t} = A*, and

**antisymmetric**if

*A*

^{t}= -AExamples:

**Exercise**: let

a) Calculate their traces

b) Find *x, y* and *z* to make *A* symmetric

c) Find *a, b* and *c* to make *B* antisymmetric

Solutions: a) tr(A) = y + 16, tr(B) = c; b) x = -1, y € **R**, z = 0; c) a = -3, b = -1, c = 0

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