A⁻¹的意思、翻譯和例句

是什麼意思

「A⁻¹」通常用於數學領域,特別是線性代數中,表示矩陣 A 的逆矩陣。逆矩陣是指一個矩陣與其逆矩陣相乘會得到單位矩陣。在這種情況下,A⁻¹ 是 A 的反轉,只有當 A 是可逆矩陣時,這個表示才有效。

依照不同程度的英文解釋

  1. The opposite of a matrix.
  2. A matrix that can undo the effect of another matrix.
  3. A matrix that, when multiplied by the original, gives a special matrix.
  4. A matrix that reverses the transformation of another matrix.
  5. A matrix that allows solving equations involving the original matrix.
  6. A matrix that, when multiplied with its corresponding matrix, yields an identity matrix.
  7. A matrix that satisfies the property of multiplication resulting in the identity matrix.
  8. A matrix that is used to solve linear equations by providing a way to reverse transformations.
  9. A matrix that exists under specific conditions and plays a crucial role in linear transformations.
  10. A mathematical construct that is essential for solving systems of equations.

相關英文單字或片語的差別與用法

1:Inverse Matrix

用法:

在數學中,逆矩陣是指一個矩陣的反轉,當它與原矩陣相乘時,會得到單位矩陣。逆矩陣的存在需要滿足一定的條件,比如原矩陣必須是方陣且行列式不為零。逆矩陣在解線性方程組和進行矩陣運算時非常重要。

例句及翻譯:

例句 1:

要解這個方程組,我們需要計算矩陣 A 的逆矩陣。

To solve this system of equations, we need to calculate the inverse matrix of A.

例句 2:

如果矩陣 A 有逆矩陣,則可以用 A⁻¹ 來解決問題。

If matrix A has an inverse matrix, we can use A⁻¹ to solve the problem.

例句 3:

逆矩陣的存在性是線性代數中的一個重要概念。

The existence of the inverse matrix is an important concept in linear algebra.

2:Reciprocal Matrix

用法:

這個詞通常不如逆矩陣常見,但在某些情況下也可以用來描述與原矩陣相互作用的矩陣。它強調的是一種反向運算的性質,儘管在數學上更精確的術語是逆矩陣。

例句及翻譯:

例句 1:

在討論矩陣運算時,我們有時會提到矩陣的倒數矩陣。

When discussing matrix operations, we sometimes refer to the reciprocal matrix.

例句 2:

理解倒數矩陣的概念對於掌握線性代數非常重要。

Understanding the concept of the reciprocal matrix is essential for mastering linear algebra.

例句 3:

在某些情況下,倒數矩陣可以幫助我們簡化計算。

In some cases, the reciprocal matrix can help simplify calculations.