MatrixDot

MatrixDot (waveA, waveB)

The MatrixDot function calculates the inner (scalar) product for two 1D waves. A 1D wave A represents a vector in the sense:

$$\displaystyle \mathbf{A}=\sum \alpha_{i} \hat{e}_{i}, \quad \hat{e}_{i} \text { is a unit vector } .$$

Given two such waves A and B, the inner product is defined as:

$$\displaystyle i p=\sum \alpha_{i} \beta_{i} .$$

When both waveA and waveB are complex and the result is assigned to a complex-valued number, MatrixDot returns

$$\displaystyle i p c=\sum \alpha_{i}^{*} \beta_{i} .$$

If you prefer the definition where the second factor is the one that is conjugated, you can simply reverse the order of waveA and waveB in the function call.

If the result is assigned to a real number, MatrixDot returns

$$\displaystyle i p=\left|\sum \alpha_{i}^{*} \beta_{i}\right| .$$

If either waveA or waveB is complex and the result is assigned to a real-valued number, MatrixDot returns

$$\displaystyle i p=\left|\sum \alpha_{i} \beta_{i}\right| .$$

When the result is assigned to a complex-valued number MatrixDot returns

$$\displaystyle i p c=\sum \alpha_{i} \beta_{i} .$$

See Also

The MatrixOp operation for more efficient matrix operations.

Matrix Math Operations for more about Igor's matrix routines.