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Glacius
Linear algebraConcept reference

Matrix entries

A matrix entry is selected by a row index followed by a column index, each counted from one.

1 min read1 figureSources & further reading
On this page 7 sections
  1. Overview
  2. An entry is one number in a matrix
  3. Indices must name an existing row and column
  4. Labels give entries meaning
  5. Key takeaway
  6. Sources & further reading
  7. Concept connections

01An entry is one number in a matrix#

An entry is one number in a matrix. The notation aija_{ij} means row ii, column jj of matrix AA. Count both from 1.

For the labelled matrix, row 2 is (0,8,2)(0,8,2). Its third entry is 2, so a23=2a_{23}=2.

Matrix A has rows (6, −1, 4) and (0, 8, 2). The highlighted entry 2 lies at row 2, column 3. Row labels increase downward from 1; column labels increase rightward from 1.Matrix A has rows (6, −1, 4) and (0, 8, 2). The highlighted entry 2 lies at row 2, column 3. Row labels increase downward from 1; column labels increase rightward from 1.
Figure 1Matrix A has rows (6, −1, 4) and (0, 8, 2). The highlighted entry 2 lies at row 2, column 3. Row labels increase downward from 1; column labels increase rightward from 1.
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Check your reasoning

Find a12a_{12}. A=[3−472]A=\begin{bmatrix}3&-4\\7&2\end{bmatrix}

Show answer and explanation
-4

Row 1, column 2 contains −4.

02Indices must name an existing row and column#

Indices must name an existing row and column. In a 2×32\times3 matrix, a23a_{23} exists; a31a_{31} does not because there is no row 3.

Check your reasoning

A=[1528]A=\begin{bmatrix}1&5\\2&8\end{bmatrix}. Find a31a_{31}.

  1. A2
  2. B8
  3. CNo such entry
Show answer and explanation
No such entry

There is no third row.

03Labels give entries meaning#

Labels give entries meaning. If rows list people and columns list measurements, choose the person’s row and the measurement’s column using the declared orders.

Check your reasoning

Rows: (Ada, Bo). Columns: (cats, dogs). Value for Bo, dogs? [2143]\begin{bmatrix}2&1\\4&3\end{bmatrix}

Show answer and explanation
3

Row 2, column 2: 3.

Key takeaway

Read the first index as row and the second as column.

  • Retrieve a matrix entry using its row and column indices.

Sources & further reading

  1. [1]

Reference this concept

Link to this page, a section, or an individual figure.

Glacius. “Matrix entries.” Math behind ML. /learn/la-index