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What is associative algebra?
Associative algebra is a branch of mathematics that studies algebraic structures known as algebras, where the operations of addition and multiplication satisfy the associative property. In these algebras, elements can be combined using a bilinear multiplication operation, which means that the product of two elements is linear in each argument. Associative algebras can be defined over various fields, such as real or complex numbers, and they play a crucial role in various areas of mathematics, including representation theory, functional analysis, and quantum mechanics. An important example of associative algebras is matrix algebras, where matrices form an algebra under standard matrix addition and multiplication.
What is the condition for the addition of matrices?
The matrices must have the same dimensions.
Do all matrices have determinant?
Only square matrices have a determinant
What is the synonym of associative property?
There is no synonym for the associative properties.
How are associative and commutative proerties alike and different?
They are alike in so far as they are properties of binary operations on elements of sets. T The associative property states that order in which operations are evaluated does not affect the result, while the commutative property states that the order of the operands does not make a difference. Basic binary operators are addition, subtraction, multiplication, division, exponentiation, taking logarithms. Basic operands are numbers, vectors, matrices.
