Matrix operations, matrix types, and basic matrix algebra from a college linear algebra course.
About this set
35 basic cards for College Linear Algebra. Set 6 of 11 in Linear Algebra. It opens with "What is a matrix?" and "In matrix notation, what does a_ij represent?". Study it alongside the other College sets below.
35 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a matrix?
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A rectangular array of numbers arranged in rows and columns.- In matrix notation, what does a_ij represent?
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The element in the i-th row and j-th column of matrix A.- What does it mean when a matrix has dimensions m by n?
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The matrix has m rows and n columns.- What is a square matrix?
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A matrix with the same number of rows and columns, where m equals n.- What is a row vector?
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A matrix with exactly one row, with dimensions 1 by n.- What is a column vector?
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A matrix with exactly one column, with dimensions m by 1.- What is the zero matrix?
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A matrix where every element equals zero.- What is the identity matrix I_n?
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An n by n matrix with ones on the main diagonal and zeros everywhere else.- What is a diagonal matrix?
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A square matrix with non-zero elements only on the main diagonal.- What is an upper triangular matrix?
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A square matrix where all entries below the main diagonal are zero.- What is a lower triangular matrix?
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A square matrix where all entries above the main diagonal are zero.- When are two matrices equal?
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When they have the same dimensions and all corresponding elements are equal.- What does it mean to multiply a matrix A by a scalar c?
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Multiply every element of A by c.- What condition must be met to add two matrices?
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The matrices must have the same dimensions.- How do you add two matrices A and B?
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Add corresponding elements: (A + B)_ij = a_ij + b_ij.
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