determinant

Meanings

• noun

  A number that can be calculated from the given set of numbers or matrix and represents the value of the determinant of that set or matrix.

  - "The determinant of a 2x2 matrix is calculated by subtracting the product of the elements in the first row and the minors of the first column from the product of the elements in the second row and the minors of the second column."
  - "The determinant of a 3x3 matrix can be found by using the formula: determinant = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)"

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Variants

List of all variants of determinant that leads to same result
determinant , determinantal , determinants , antigenic determinant , epitope , epitopes , antigenic determinants

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Etymology

origin and the way in which meanings have changed throughout history.

The term 'determinant' comes from the Latin word 'determinare', which means 'to establish definitely'. It was first introduced in mathematics by Leibniz and Cramer in the late 17th and early 18th centuries.

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Trivia

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1. The determinant of a matrix is only defined for square matrices.

2. The determinant of a matrix is equal to the product of its eigenvalues.

3. The determinant of a diagonal matrix is the product of its diagonal elements.

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Related Concepts

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1. Matrix: A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are used to represent linear transformations and systems of linear equations.

2. Minor: A minor is a submatrix obtained by deleting one or more rows and one or more columns from a given matrix.

3. Determinant of a matrix: The determinant of a square matrix is a special number that can be calculated from the given matrix and has various applications in mathematics and physics.

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Culture

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The concept of determinants has played a significant role in the development of linear algebra and matrix theory. It has applications in various fields such as physics, engineering, computer graphics, and cryptography.

How to Memorize "determinant"

1. visualize
   

   - Visualize a matrix and imagine calculating the determinant by following the steps for a 2x2 or 3x3 matrix.

2. associate
   

   - Associate the determinant with the idea of establishing definitively the value of a matrix.

3. mnemonics
   

   - Use the mnemonic 'Determinant: Delete Every Row and Minor Then Multiply' to remember the steps for calculating the determinant.

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