Dot

Generated from the engine's own definition: compute-engine's symbol, which we neither extend nor document by hand.

Dot product (vector inner product) or matrix product.

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Dot(list<tuple> | matrix | tuple | vector, list<tuple> | matrix | tuple | vector) -> valueDot product (vector inner product) or matrix product.

Typed signatures

Type	Package	Applies
(list<tuple> | matrix | tuple | vector, list<tuple> | matrix | tuple | vector) -> value	compute-engine	always
(expression<ModularMatrix> | list<tuple> | matrix | matrix | string | tuple | tuple | vector | vector, expression<ModularMatrix> | list<tuple> | matrix | matrix | string | tuple | tuple | vector | vector) -> expression<ModularMatrix> | matrix | number | value | vector	modularreplaces compute-engine	always

Domain: Compute engine

Examples

Basic #

Vector dot product, symbolic

live ↗

In$\mathrm{Dot}(\bigl\lbrack a, b, c\bigr\rbrack, \bigl\lbrack x, y, z\bigr\rbrack)$Out$ax+by+cz$

Matrix times vector gives a vector

live ↗

In$\mathrm{Dot}(\bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack c, d\bigr\rbrack\bigr\rbrack, \bigl\lbrack x, y\bigr\rbrack)$Out$\bigl\lbrack ax+by, cx+dy\bigr\rbrack$

Vector times matrix uses the columns

live ↗

In$\mathrm{Dot}(\bigl\lbrack x, y\bigr\rbrack, \bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack c, d\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack ax+cy, bx+dy\bigr\rbrack$

Scope #

Integer vectors give an exact scalar

live ↗

In$\mathrm{Dot}(\bigl\lbrack1, 2, 3, 4, 5\bigr\rbrack, \bigl\lbrack1, 8, 9, 0, -1\bigr\rbrack)$Out$39$

Matrix product with exact rational entries

live ↗

In$\mathrm{Dot}(\bigl\lbrack\bigl\lbrack2, 0, 0\bigr\rbrack, \bigl\lbrack0, 0, \frac{35}{2}\bigr\rbrack, \bigl\lbrack0, \frac{35}{2}, 0\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack8, 0, 0\bigr\rbrack, \bigl\lbrack0, 0, 10\bigr\rbrack, \bigl\lbrack0, 10, 0\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack16, 0, 0\bigr\rbrack, \bigl\lbrack0, 175, 0\bigr\rbrack, \bigl\lbrack0, 0, 175\bigr\rbrack\bigr\rbrack$

live ↗

In$\mathrm{Dot}(\bigl\lbrack a, b, c\bigr\rbrack, \bigl\lbrack0, b, d+k\bigr\rbrack)$Out$b^2+cd+ck$

About

Examples	6
Checked against	Wolfram Language 6 agree
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