matrix addition

Thân thiện

Two students perform matrix addition on the whiteboard.

Definition

Noun: - The operation of adding two matrices: "Matrix addition" is a mathematical operation where two matrices of the same dimensions are added together by adding their corresponding entries.

Usage

Matrix addition is a fundamental operation in linear algebra. It is only defined for matrices that have the same number of rows and the same number of columns. The result is a new matrix of the same dimensions.

Examples

• Noun:
  • Matrix addition is performed element by element.
  • Before you can perform matrix addition, you must check that the matrices have identical dimensions.
  • The properties of matrix addition, such as commutativity and associativity, are similar to those of regular number addition.

Advanced Usage

• "to be closed under matrix addition": A set of matrices is closed under this operation if adding any two matrices from the set produces another matrix within the same set.
  • The set of all 2x2 matrices with real entries is closed under matrix addition.

Variants and Related Words

• Matrix (n): A rectangular array of numbers, symbols, or expressions arranged in rows and columns.
• Addend (n): In the context of matrix addition, each of the matrices being added is an addend.
• Sum matrix (n): The resulting matrix from an operation of matrix addition.

Synonyms

• Matrix sum operation: A less common but descriptive synonym for matrix addition.

Related Phrases

• Element-wise addition: This phrase describes the precise method of matrix addition, emphasizing that the operation is applied to each corresponding pair of elements.
  • Matrix addition is a form of element-wise addition.

Học thuật

Noun

1. the addition of matrices