Vectors, matrices, eigenvalues, and vector space concepts from an introductory college linear algebra course.
40 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a vector?
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An ordered list of numbers (or scalars) arranged in a specific sequence.- What does it mean for two vectors to be parallel?
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One vector is a scalar multiple of the other.- Define the dot product of two vectors.
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The sum of the products of their corresponding components.- What is the norm (or length) of a vector?
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The square root of the sum of the squares of its components.- Define orthogonal vectors.
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Vectors whose dot product is zero.- What is a matrix?
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A rectangular array of numbers organized in rows and columns.- What is the transpose of a matrix?
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The matrix obtained by swapping its rows and columns.- When can two matrices be multiplied together?
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When the number of columns in the first equals the number of rows in the second.- Define the identity matrix.
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A square matrix with ones on the main diagonal and zeros elsewhere.- What is the determinant?
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A scalar value computed from a square matrix that encodes scaling and orientation properties.- What does a zero determinant indicate about a matrix?
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The matrix is singular (non-invertible).- What is an invertible matrix?
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A square matrix that has a multiplicative inverse (A * A inverse = I).- Define an eigenvalue.
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A scalar lambda such that Av = lambda*v for some non-zero vector v.- Define an eigenvector.
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A non-zero vector v such that Av = lambda*v for some scalar lambda.- What is an eigenspace?
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The set of all eigenvectors corresponding to a particular eigenvalue, plus the zero vector.
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