Subspaces Study guides, Class notes & Summaries
Looking for the best study guides, study notes and summaries about Subspaces? On this page you'll find 52 study documents about Subspaces.
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MATH 133 - basically everything (summary)
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Summary of all the important topics from MATH133 - including vector spaces, subspaces, eigenstuff and lots more.
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Which of the following subsets of R33 are subspaces of R3x3.2
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Which of the following subsets of R33 are subspaces of R3x3.2
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Linear Algebra Practice Problems Set 4
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The following document contains the problem statements and problem solutions for a selection of questions related to linear algebra. The focus of the questions is around finding the Basis and Dimensions for the Subspaces of a matrix. It also includes how to find the particular, special and complete solution to a set of linear equations or matrix equation. The document corresponds with the teachings of the listed textbook, Introduction to Linear Algebra. Please do not copy the problem solutions, ...
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Linear Algebra Practice Problems Set 5
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The following document contains the problem statements and problem solutions for a selection of questions related to linear algebra. The focus of the questions is around finding the Basis and Dimensions for the Subspaces of a matrix. This includes the column space, row space, null space, and left null space. It also includes how to find the particular, special and complete solution to a set of linear equations or matrix equation. The document corresponds with the teachings of the listed textbook...
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Linear Algebra 1 - Subspaces
- Class notes • 13 pages • 2022
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Notes on subspaces of vector spaces including examples, their operations, respective theorems and propositions as well as visual representations.
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MA 262: 4.4-4.5 Review- Bases & Dimensions of Vector Spaces, Row & Column Spaces
- Class notes • 4 pages • 2024
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Review of lesson 4.4-4.5 for MA 262 (Linear Algebra & Differential Equations) at Purdue University. Content based on class textbook Differential Equations & Linear Algebra by C. Henry Edwards and David E. Penney (ISBN: 9780536264923). 
4.4 covers bases and dimensions of vector spaces, including the definition(s) of a basis of a vector space, the standard basis of R^n, finite vs. infinite dimensionals, and relationships between bases, span, linear independence, and number of vectors in a set. De...
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MA 262 (Linear Algebra & Differential Equations) Ch. 4 Notes
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Package includes all summary sheets for Ch. 4 of MA 262 at Purdue University. Specifically, notes for Lessons 4.1 (Vector Spaces), 4.2 (The Vector Space R^n & Subspaces), 4.3 (Linear Combinations & Independence of Vectors), 4.4 (Bases & Dimensions of Vector Spaces), & 4.5 (Row & Column Spaces). All lesson reviews include example problems.
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MA 262: Final Review- Methods & Insights for Select Problems
- Class notes • 4 pages • 2024
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Review for MA 262 (Linear Algebra & Differential Equations) final at Purdue University. Content based on past exam questions. 
Compilation of past exam questions and solutions for complex problems with methods + rationale. Topics covered include determinant properties, bases, method of undetermined coefficients, variation of parameters, null space, vector spaces/subspaces, homogeneous/nonhomogeneous linear systems, row and column rank, and mechanical vibrations.
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Primary Decomposition Theorem
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Includes: 
Statement and proof of Primary Decomposition Theorem 
 
Primary decomposition theorem from associated prime. 
It uses minimal polynomial of a matrix to write a vector space as a direct sum of invariant subspaces.
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Stanford UniversitySTATS 231hw0-solutions
- Exam (elaborations) • 10 pages • 2021
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Homework 0 solutions 
CS229T/STATS231 
1. Linear algebra (0 points) 
a (dual norm of L1 norm) The L1 norm k · k1 of a vector v 2 Rn is defined as 
kvk1 = 
nX i 
=1 
jvij: (1) 
The dual norm k · k∗ of a norm k · k is defined as 
kvk∗ = sup 
kwk≤1 
(v · w): (2) 
Compute the dual norm of the L1 norm. (Here v · w denotes the inner product between v and w: v · w , 
Pn i=1 viwi) 
Solution: 
We will prove that 
sup 
kwk1≤1 
(v · w) = max 
i2[n] 
vi = kvk1 (3) 
which implies that the dua...
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