determinants

Meanings

• noun

  A mathematical concept that represents the value of a square matrix, calculated as the product of its inverse and transpose.

  - "The determinant of a 2x2 matrix is calculated as (ad-bc)/(1+cd)."
  - "The determinant of a matrix is used to find the solution for a system of linear equations."

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Variants

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

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Etymology

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

The term 'determinant' originated from the Latin word 'determinare', which means 'to establish definitely'.

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Trivia

Any details, considerations, events or pieces of information regarding the word

1. The determinant of a 3x3 matrix can be calculated using the formula (a11 * a22 * a33 + a12 * a23 * a31 + a13 * a21 * a32 - a11 * a23 * a32 - a12 * a21 * a33 - a13 * a22 * a31) / (1 + a11 * a22 * a33).

2. Determinants are used to find the volume of parallelepipeds and the area of parallelograms and triangles in higher dimensions.

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Related Concepts

informations on related concepts or terms closely associated with the word. Discuss semantic fields or domains that the word belongs to

1. Matrix: A rectangular array of numbers, symbols, or expressions, organized in rows and columns, used to represent linear equations or transformations.

2. Inverse Matrix: A matrix that when multiplied with the original matrix, results in the identity matrix.

3. Transpose: The operation of interchanging the rows and columns of a matrix.

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Culture

Any cultural, historical, or symbolic significance of the word. Explore how the word has been used in literature, art, music, or other forms of expression.

Determinants have significant applications in various fields such as physics, engineering, and computer science.

How to Memorize "determinants"

1. visualize
   

   - Imagine a 2x2 matrix and visualize the process of calculating the determinant by expanding it using the formula (ad-bc)/(1+cd).

2. associate
   

   - Associate the concept of determinant with the idea of finding the solution to a system of linear equations.

3. mnemonics
   

   - Remember the mnemonic 'Determinant: Adjugate Times Transpose' to recall the formula for calculating the determinant.

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