determinant

/dɪˈtɜːmɪnənt/ (bre, ipa) · /dɪˈtɜːrmɪnənt/ (ame, ipa) · /di-ˈtər-mə-nənt/ (ame, mw)

determinant — 名詞

  • determinantsingular
  • determinantsplural

1. a condition, event, or quality that plays an important part in shaping how a sit

1.名詞C1
釋義

決定因素

影響結果的關鍵條件

a condition, event, or quality that plays an important part in shaping how a situation turns out

例句

High rent was the main determinant of where Aaron's family moved in Taipei.

高房租是 Aaron 家搬到台北哪一區的主要決定因素。

main determinant of + wh-clause

Noor said cost was the key determinant when her team chose new laptops.

Noor 說，成本是她的團隊挑選新筆電時的關鍵決定因素。

key determinant when making a choice

同義詞
  • factor

    broader and more neutral; determinant sounds more technical and often suggests stronger influence

  • driver

    common in business or policy writing for a force that pushes change forward

  • influence

    can be weaker or less direct than a determinant

  • predictor

    used when something helps forecast a result, not necessarily cause it

文法句型

determinant of + noun/wh-clause

a key/main determinant of + noun

用法筆記

More formal than factor and common in research, policy, and business writing. It usually points to one influence among several and often appears in phrases like key determinant of or main determinant of.

常見錯誤

❌Price was a determinant for I bought the ticket.
✅Price was a determinant of my decision to buy the ticket.
💡determinant is usually followed by of when you name the result it influences.

2. in mathematics, a single number found from the entries of a square matrix, often

2.名詞C2
釋義

行列式

由方陣算出的單一數值

in mathematics, a single number found from the entries of a square matrix, often used to check whether the matrix has an inverse or whether related equations can be solved

例句

Professor Aaron wrote the determinant beside the matrix before starting the proof.

Aaron 教授在開始證明前，先把那個行列式寫在矩陣旁邊。

the determinant of a matrix

Jin found the determinant first, then checked whether the system had one solution.

Jin 先求出行列式，再檢查那組方程式是否只有一個解。

find the determinant first

文法句型

the determinant of + matrix

calculate/find the determinant

用法筆記

Used in algebra with square matrices, especially in phrases like the determinant of the matrix. A zero determinant often shows that the matrix has no inverse, so teachers use it when discussing invertibility and systems of equations.

常見錯誤

❌The determinant is the matrix.
✅The determinant is a number calculated from the matrix.
💡the determinant comes from the matrix, but it is not the matrix itself.
❌I found the determinant of this rectangular matrix.
✅I found the determinant of this square matrix.
💡determinants are normally defined for square matrices in basic linear algebra.