Matrix Computations, Introduction


For this discussion, a scalar is a real or complex number. A matrix is a rectangular array of scalars arranged in m rows and n columns. The element in row i and column j is labeled as element i, j with 1 <= i <= m, 1 <= j <= n. A one by one matrix is not considered to be a scalar and a scalar is not a matrix. An m by n matrix A can be represented as {a11, a12, ..., a1n; a21, a22, ..., a2n; ... am1, am2, ... amn} or

| a11 a12 ... a1n |
| a21 a22 ... a2n |
| ... ............... ... |
| am1 am2 ... amn |

An m by 1 matrix is a column vector. A 1 by n matrix is a row vector. A polynomial P(x) = p(n)*x^n + p(n−1)*x^(n−1) + ... + p(1)*x + p(0) can be represented as an (n + 1) by 1 column vector {p(n); p(n−1); ..., p(1); p(0)}.

The number of rows in a matrix A can be referred to as A.m, the number of Columns as A.n. The size of a matrix is a 1 by 2 matrix, Size(A) = {A.m, A.n}.

See: Matrix -- From MathWorld

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