Arithmetic Operators (MATRIX-END MATRIX command)

You can add, subtract, multiply, or exponentiate matrices according to the rules of matrix algebra, or you can perform elementwise arithmetic, in which you multiply, divide, or exponentiate each element of a matrix separately. The arithmetic operators are listed below.

Unary −. Sign reversal. A minus sign placed in front of a matrix reverses the sign of each element. (The unary + is also accepted but has no effect.)

+. Matrix addition. Corresponding elements of the two matrices are added. The matrices must have the same dimensions, or one must be a scalar.

−. Matrix subtraction. Corresponding elements of the two matrices are subtracted. The matrices must have the same dimensions, or one must be a scalar.

*. Multiplication. There are two cases. First, scalar multiplication: if either of the matrices is a scalar, each element of the other matrix is multiplied by that scalar. Second, matrix multiplication.

/. Division. The division operator performs elementwise division (described below). True matrix division, the inverse operation of matrix multiplication, is accomplished by taking the INV function (square matrices) or the GINV function (rectangular matrices) of the denominator and multiplying.

**. Matrix exponentiation. A matrix can be raised only to an integer power. The matrix, which must be square, is multiplied by itself as many times as the absolute value of the exponent. If the exponent is negative, the result is then inverted.

&*. Elementwise multiplication. Each element of the matrix is multiplied by the corresponding element of the second matrix. The matrices must have the same dimensions, or one must be a scalar.

&/. Elementwise division. Each element of the matrix is divided by the corresponding element of the second matrix. The matrices must have the same dimensions, or one must be a scalar.

&**. Elementwise exponentiation. Each element of the first matrix is raised to the power of the corresponding element of the second matrix. The matrices must have the same dimensions, or one must be a scalar.

:. Sequential integers. This operator creates a vector of consecutive integers from the value preceding the operator to the value following it. You can specify an optional increment following a second colon. See Matrix Notation Shorthand (MATRIX-END MATRIX command) for the principal use of this operator.

• Use these operators only with numeric matrices. The results are undefined when they are used with string matrices.