Matrix operations
The vocabulary of matrices (dimensions, entries, special matrices) and the entry-by-entry operations: sum, multiplication by a real number and transpose.
- 26 cards
- 5 topics
- Free
The outline, topic by topic
Each topic is weighted the way the exam weighs it.
- Concepts
- Questions
- Sort and link
- The numbers
- Understand
A few cards from the deck
Dimensions of a matrix: what is it?
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The pair m × n made of the number of rows m, then the number of columns n.
Rows are always counted first: a matrix with 3 rows and 4 columns has dimensions 3 × 4, and 12 entries.
What is the value of a_32 in the matrix (1 2 3 4), (5 6 7 8), (9 10 11 12)?
107116
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10a_32 is in row 3, column 2: that is 10. The 7 is in row 2, column 3 (indices swapped), and the 11 is in row 3, column 3.
An … matrix is a square matrix whose entries below the diagonal are all zero.
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An upper triangular matrix is a square matrix whose entries below the diagonal are all zero.
A diagonal matrix is both upper and lower triangular. The entries on the diagonal can be anything.
Entry a_ij: what is it?
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The number located in the i-th row and the j-th column of the matrix A.
The first index is the row, the second the column: a_23 is in row 2 and column 3, not the other way round.