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2. Zero-product property - Wikipedia

   en.wikipedia.org/wiki/Zero-product_property

   In algebra, the zero-product property states that the product of two nonzero elements is nonzero. In other words, =, = = This property is also known as the rule of zero product, the null factor law, the multiplication property of zero, the nonexistence of nontrivial zero divisors, or one of the two zero-factor properties.

3. Multiplication - Wikipedia

   en.wikipedia.org/wiki/Multiplication

   Multiplication (often denoted by the cross symbol ×, by the mid-line dot operator ⋅, by juxtaposition, or, on computers, by an asterisk *) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product .

4. Dot product - Wikipedia

   en.wikipedia.org/wiki/Dot_product

   Dot product. In mathematics, the dot product or scalar product[ note 1] is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors ), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or ...

5. Product (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Product_(mathematics)

   Product (mathematics) In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors. For example, 21 is the product of 3 and 7 (the result of multiplication), and is the product of and (indicating that the two factors should be multiplied together).

6. Tensor product - Wikipedia

   en.wikipedia.org/wiki/Tensor_product

   The tensor product of two vector spaces is a vector space that is defined up to an isomorphism.There are several equivalent ways to define it. Most consist of defining explicitly a vector space that is called a tensor product, and, generally, the equivalence proof results almost immediately from the basic properties of the vector spaces that are so defined.

7. Cross product - Wikipedia

   en.wikipedia.org/wiki/Cross_product

   If the cross product of two vectors is the zero vector (that is, a × b = 0), then either one or both of the inputs is the zero vector, (a = 0 or b = 0) or else they are parallel or antiparallel (a ∥ b) so that the sine of the angle between them is zero (θ = 0° or θ = 180° and sin θ = 0). The self cross product of a vector is the zero ...

8. Commutative property - Wikipedia

   en.wikipedia.org/wiki/Commutative_property

   In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a property of arithmetic, e.g. "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more ...

9. Trace (linear algebra) - Wikipedia

   en.wikipedia.org/wiki/Trace_(linear_algebra)

   Trace (linear algebra) In linear algebra, the trace of a square matrix A, denoted tr (A), [1] is defined to be the sum of elements on the main diagonal (from the upper left to the lower right) of A. The trace is only defined for a square matrix ( n × n ). In mathematical physics texts, if tr (A) = 0 then the matrix is said to be traceless.