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Linear Algebra
University of California - Davis
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Ruoguang Tian

Vazirani Monica

4

Robert Krone

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Class Notes

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MAT 22A Lecture 1: MAT 22A_ Lecture 1-4, 1.1 Vector and Linear Combinations, 1.2 Lengths and Dot Products, 1.3 Matrices

MAT 22A Lecture Notes - Lecture 1: Linear Combination, Scalar Multiplication, Euclidean Vector

MAT 22A Lecture 2: Lec Sept28 3

MAT 22A Lecture 2: MAT 22A Tian

MAT 22A Lecture 2: Lec Sept28 2

MAT 22A Lecture 2: MAT 22A

MAT 22A Lecture Notes - Lecture 2: Dot Product, Junkers J.I, Vril

MAT 22A Lecture 2: MAT 22A Tian

MAT 22A Lecture 2: Lec Sept28 1

MAT 22A Lecture Notes - Lecture 3: Triangle Inequality, Institution Of Engineering And Technology, Linear Combination

MAT 22A Lecture Notes - Lecture 4: Linear Independence, Xz, Linear Combination

MAT 22A Lecture 5: MAT 22A_ Lecture 5 , 2.1 Vectors and Linear Equations, 2.2 The Idea of Elimination

MAT 22A Lecture Notes - Lecture 5: Linear Combination, Coefficient Matrix

I row view ) ( column view ) D case the now view is more intuitive than the column view . However , in higher dimensions the column view is more intuit

MAT 22A Lecture Notes - Lecture 6: Triangular Matrix, Linear Combination

MAT 22A Lecture Notes - Lecture 7: Triangular Matrix, Ibm System I

In general to solve an mln systems of eqns , elimination proceeds as follows : 1st egn to create zeros below the first pivot. Continue until you get up

MAT 22A Lecture Notes - Lecture 8: Elementary Matrix, Identity Matrix, Mexican Peso

MAT 22A Lecture Notes - Lecture 9: Mull, Ebi, Thx

MAT 22A Lecture 10: Lecture10

= (f) e3 d way of matrix mutt. A , b of the same size , we have addition laws. Ca t c t c b i distributivity for. B , c of appropriate sizes , we have

MAT 22A Lecture Notes - Lecture 11: Augmented Matrix

MAT 22A Lecture Notes - Lecture 12: Permutation Matrix, Diagonal Matrix

MAT 22A Lecture Notes - Lecture 13: Diagonally Dominant Matrix, Diagonal Matrix, Triangular Matrix

MAT 22A Lecture Notes - Lecture 14: Hne, Asteroid Family

MAT 22A Lecture 15: lecture15

MAT 22A Lecture Notes - Lecture 16: Triangular Matrix, Emic And Etic

MAT 22A Lecture Notes - Lecture 17: Euclidean Vector, Zuko, Thx

If a is invertible then there exists a permutation matrix p to put news of a in proper order to factor. = ( f to) , matrix p=f !iff ) choose perm . pat

MAT 22A Lecture Notes - Lecture 18: Linear Combination

MAT 22A Lecture Notes - Lecture 19: Speedstep

MAT 22A Lecture Notes - Lecture 20: Row Echelon Form, Triangular Matrix, Mexican Peso

R for both row echelon form and now reduced echelon form. Uses upper triangular form and now echelon form interchangeably. A is in row echelon form if

MAT 22A Lecture Notes - Lecture 27: Mexican Peso, Sodium Hydride, Row Echelon Form

How to find the null space of any mxn matrix. A and express it in terms of special sins. If a is invertible exactly one so i n. Faff an is trivial nxn

MAT 22A Lecture Notes - Lecture 28: Mexican Peso, Linear Combination, Row And Column Spaces

Vectors does their span get smaller if one. Vt removed is th is linearly independent if and only it. The only coefficients that satisfy the equation .

MAT 22A Lecture Notes - Lecture 29: Dot Product, Mexican Peso, Orthogonal Complement

T and w of a vector space are in. V is perpendicular to every vector w in w he. T o for all t in v and all inin w . A the null space mai and the row sp

MAT 22A Lecture Notes - Lecture 30: Linear Combination, Qtq, Qi

MAT 22A Lecture Notes - Lecture 31: Orthonormality, Detent, Determinant

Jn and we want to find orthonormal vectors gin. Orthonormal vectors are also linearly independent , and much easier to work with. I it , e projection o

MAT 22A Lecture Notes - Lecture 32: Invertible Matrix

A is singular then de - hai o. A is invertible then det aho and detox. We analyze how an nxn matrix transform a vector. At compare tox ( both in ry ? r