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Math 102 Winter 2022
Terminology and Theorems
Updated 1/3/22
Note: The following list is a minimal collection of the important terms and theorems for this course.
You simply must be familiar with them and how they are used: in the case of theorems, you should
be familiar with how they are proved. This basic knowledge is analogous to the vocabulary of a language: it
is impossible to speak the language without it.
- Math 18 Terminology
- A list of terminology you should know from Math 18 (or your previous linear algebra course). Please review!
- Section 1.6
- partitioned matrix
- blocks
- block multiplication
- scalar product; inner product
- outer product
- Section 3.5
- coordinates; coordinate vector
- transition matrix
- Chapter 4
- linear transformation; linear operator
- kernel
- image; range
- matrix representation
- standard matrix representation
- matrix representing a linear transformation with respect to ordered bases
- similar
- Chapter 5
- scalar product
- length
- distance
- Cauchy-Schwarz inequality
- orthogonal vectors
- scalar projection
- vector projection
- Pythagorean law
- orthogonal subspaces
- orthogonal complement
- Fundamental Subspaces Theorem
- direct sum
- normal equations
- least squares solution
- projection matrix
- inner product; inner product space
- Pythagorean law
- scalar projection
- vector projection
- Cauchy-Schwarz Inequality
- norm
- distance
- orthogonal set
- orthonormal set; orthonormal basis
- orthogonal matrix
- permutation matrix
- projection matrix
- the Gram-Schmidt process
- Gram-Schmidt QR factorization
- Chapter 6
- eigenvalue
- eigenvector
- eigenspace
- characteristic polynomial; characteristic equation
- diagonalizable
- defective matrix
- exponential of a matrix
- complex inner product
- Hermitian matrix
- unitary matrix
- Schur's Theorem
- Spectral Theorem
- invariant subspace
- the Real Schur Decomposition
- Spectral Theorem for Real Symmetric Matrices
- normal matrix
- singular values
- singular value decomposition (SVD)
- The SVD Theorem
- right singular vectors
- left singular vectors
- compact form of the SVD
- Section 7.7
- pseudoinverse; Moore-Penrose pseudoinverse
- the Penrose conditions
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