Elementary Linear Algebra with Applications. Third Edition
Elementary Linear Algebra with Applications. Third Edition
Overview
Preface. List of Applications. 1. Introduction to Linear Equations and Matrices. Introduction to Linear Systems and Matrices. Gaussian Elimination. The Algebra of Matrices: Four Descriptions of the Product. Inverses and Elementary Matrices. Gaussian Elimination as a Matrix Factorization. Transposes, Symmetry, and Band Matrices: An Application. Numerical and Programming Considerations: Partial Pivoting, Overwriting Matrices, and Ill-Conditioned Systems. Review Exercises. 2. Determinants. The Determinant Function. Properties of Determinants. Finding det A Using Signed Elementary Products. Cofactor Expansion: Cramer's Rule. Applications. Review Exercises. 3. Vector Spaces. Vectors in 2- and 3-Spaces. Euclidean n-Space. General Vector Spaces. Subspaces, Span, Null Spaces. Linear Independence. Basis and Dimension. The Fundamental Subspaces of a Matrix; Rank. Coordinates and Change of Basis. An Application: Error-Correcting Codes. Review Exercises. Cumulative Review Exercises. 4. Linear Transformations, Orthogonal Projections and Least Squares. Matrices as Linear Transformation. Relationships Involving Inner Products. Least Squares and Orthogonal Projections. Orthogonal Bases and the Gram-Schmidt Process. Orthogonal Matrices, QR Decompositions, and Least Squares (Revisited). Encoding the QR Decompositions: A Geometric Approach. General Matrices of Linear of Linear Transformations; Similarity. Review Exercises. Cumulative Review Exercises. 5. Eigenvectors and Eigenvalues. A Brief Introduction to Determinants. Eigenvalues and Eigenvectors. Diagonalization. Symmetric Matrices. An Application - Difference Equations: Fibonacci Sequences and Markov Processes. An Application -Differential Equations. An Application -- Quadratic Forms. Solving the Eigenvalue Problem Numerically. Review Exercises. Cumulative Review Exercises. 6. Further Directions. Function Spaces. The Singular Value Decomposition -- Generalized Inverses, the General Least-Squares Problem, and an Approach to Ill-Conditioned Systems. Iterative Method. Matrix Norms. General Vector Spaces and Linear Transformations Over an Arbitrary Field. Review Exercises. Appendix A: More on LU Decompositions. Appendix B: Counting Operations and Gauss-Jordan Elimination. Appendix C: Another Application. Appendix D: Introduction to MATLAB and Projects. Bibliography and Further Readings. Index.Description
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Overview
Preface. List of Applications. 1. Introduction to Linear Equations and Matrices. Introduction to Linear Systems and Matrices. Gaussian Elimination. The Algebra of Matrices: Four Descriptions of the Product. Inverses and Elementary Matrices. Gaussian Elimination as a Matrix Factorization. Transposes, Symmetry, and Band Matrices: An Application. Numerical and Programming Considerations: Partial Pivoting, Overwriting Matrices, and Ill-Conditioned Systems. Review Exercises. 2. Determinants. The Determinant Function. Properties of Determinants. Finding det A Using Signed Elementary Products. Cofactor Expansion: Cramer's Rule. Applications. Review Exercises. 3. Vector Spaces. Vectors in 2- and 3-Spaces. Euclidean n-Space. General Vector Spaces. Subspaces, Span, Null Spaces. Linear Independence. Basis and Dimension. The Fundamental Subspaces of a Matrix; Rank. Coordinates and Change of Basis. An Application: Error-Correcting Codes. Review Exercises. Cumulative Review Exercises. 4. Linear Transformations, Orthogonal Projections and Least Squares. Matrices as Linear Transformation. Relationships Involving Inner Products. Least Squares and Orthogonal Projections. Orthogonal Bases and the Gram-Schmidt Process. Orthogonal Matrices, QR Decompositions, and Least Squares (Revisited). Encoding the QR Decompositions: A Geometric Approach. General Matrices of Linear of Linear Transformations; Similarity. Review Exercises. Cumulative Review Exercises. 5. Eigenvectors and Eigenvalues. A Brief Introduction to Determinants. Eigenvalues and Eigenvectors. Diagonalization. Symmetric Matrices. An Application - Difference Equations: Fibonacci Sequences and Markov Processes. An Application -Differential Equations. An Application -- Quadratic Forms. Solving the Eigenvalue Problem Numerically. Review Exercises. Cumulative Review Exercises. 6. Further Directions. Function Spaces. The Singular Value Decomposition -- Generalized Inverses, the General Least-Squares Problem, and an Approach to Ill-Conditioned Systems. Iterative Method. Matrix Norms. General Vector Spaces and Linear Transformations Over an Arbitrary Field. Review Exercises. Appendix A: More on LU Decompositions. Appendix B: Counting Operations and Gauss-Jordan Elimination. Appendix C: Another Application. Appendix D: Introduction to MATLAB and Projects. Bibliography and Further Readings. Index.Description
Condition Guidelines
Books - New and Used
The following guidelines apply to books:
- New: A brand-new copy with cover and original protective wrapping intact. Books with markings of any kind on the cover or pages, books marked as "Bargain" or "Remainder," or with any other labels attached, may not be listed as New condition.
- Used - Good: All pages and cover are intact (including the dust cover, if applicable). Spine may show signs of wear. Pages may include limited notes and highlighting. May include "From the library of" labels. Shrink wrap, dust covers, or boxed set case may be missing. Item may be missing bundled media.
- Used - Acceptable: All pages and the cover are intact, but shrink wrap, dust covers, or boxed set case may be missing. Pages may include limited notes, highlighting, or minor water damage but the text is readable. Item may but the dust cover may be missing. Pages may include limited notes and highlighting, but the text cannot be obscured or unreadable.
Note: Some electronic material access codes are valid only for one user. For this reason, used books, including books listed in the Used – Like New condition, may not come with functional electronic material access codes.
Shipping & Delivery
Shipping Fees
- Stevens Books offers FREE SHIPPING everywhere in the United States for ALL non-book orders, and $3.99 for each book.
- Packages are shipped from Monday to Friday.
- No additional fees and charges.
Delivery Times
The usual time for processing an order is 24 hours (1 business day), but may vary depending on the availability of products ordered. This period excludes delivery times, which depend on your geographic location.
Estimated delivery times:
- Standard Shipping: 5-8 business days
- Expedited Shipping: 3-5 business days
Shipping method varies depending on what is being shipped.
Tracking
All orders are shipped with a tracking number. Once your order has left our warehouse, a confirmation e-mail with a tracking number will be sent to you. You will be able to track your package at all times.
Damaged Parcel
If your package has been delivered in a PO Box, please note that we are not responsible for any damage that may result (consequences of extreme temperatures, theft, etc.).
If you have any questions regarding shipping or want to know about the status of an order, please contact us or email to support@stevensbooks.com.
Returns & Refunds
You may return most items within 30 days of delivery for a full refund.
To be eligible for a return, your item must be unused and in the same condition that you received it. It must also be in the original packaging.
Several types of goods are exempt from being returned. Perishable goods such as food, flowers, newspapers or magazines cannot be returned. We also do not accept products that are intimate or sanitary goods, hazardous materials, or flammable liquids or gases.
Additional non-returnable items:
- Gift cards
- Downloadable software products
- Some health and personal care items
To complete your return, we require a tracking number, which shows the items which you already returned to us.
There are certain situations where only partial refunds are granted (if applicable)
- Book with obvious signs of use
- CD, DVD, VHS tape, software, video game, cassette tape, or vinyl record that has been opened
- Any item not in its original condition, is damaged or missing parts for reasons not due to our error
- Any item that is returned more than 30 days after delivery
Items returned to us as a result of our error will receive a full refund,some returns may be subject to a restocking fee of 7% of the total item price, please contact a customer care team member to see if your return is subject. Returns that arrived on time and were as described are subject to a restocking fee.
Items returned to us that were not the result of our error, including items returned to us due to an invalid or incomplete address, will be refunded the original item price less our standard restocking fees.
If the item is returned to us for any of the following reasons, a 15% restocking fee will be applied to your refund total and you will be asked to pay for return shipping:
- Item(s) no longer needed or wanted.
- Item(s) returned to us due to an invalid or incomplete address.
- Item(s) returned to us that were not a result of our error.
You should expect to receive your refund within four weeks of giving your package to the return shipper, however, in many cases you will receive a refund more quickly. This time period includes the transit time for us to receive your return from the shipper (5 to 10 business days), the time it takes us to process your return once we receive it (3 to 5 business days), and the time it takes your bank to process our refund request (5 to 10 business days).
If you need to return an item, please Contact Us with your order number and details about the product you would like to return. We will respond quickly with instructions for how to return items from your order.
Shipping Cost
We'll pay the return shipping costs if the return is a result of our error (you received an incorrect or defective item, etc.). In other cases, you will be responsible for paying for your own shipping costs for returning your item. Shipping costs are non-refundable. If you receive a refund, the cost of return shipping will be deducted from your refund.
Depending on where you live, the time it may take for your exchanged product to reach you, may vary.
If you are shipping an item over $75, you should consider using a trackable shipping service or purchasing shipping insurance. We don’t guarantee that we will receive your returned item.
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