Let \m and \n be two positive integers. A \m&times'\n matrix
is a table of \m\n elements arrayed in \m lignes and \n colonnes. 
The matrix is real if the elements are real numbers, or
complex if they are complex numbers, etc.

For example, \([1,pi;e,-3]) is a real 2×2 matrix, and
\([1,i,3;4,5,pi-i;-i,-1,-1]) is a complex 3×3 matrix.

One may write a general \m×\n matrix by
 
\embed{matmn}{A = }

or abridged to (\a\i\j). The \a\i\j
are called coefficients of A, and \m×\n is its dimension.

Two matrices A and B are equal only if they are of the same dimension,
and have the same coefficient at every corresponding position.

\fold{matdefs}

To calculate a matrix, here is an online tool.
\calcform{alg/lin/matrix}

The \link{matdefs,trace,trace} of matrices satisfies the formula
 
   \(trace(AB)=trace(BA))

when \(AB) and \(BA) both make sense.

\fold{Preuve_trace_comm}

some exercises on matrices:
\exercise{cmd=new&module=U1/algebra/oefmatrix.en} 
\exercise{cmd=new&session=robot&module=U1/algebra/dialmatrix.en}