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Dr. Mathaholic

Linear Algebra

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81 items
Last updated on Dec 31, 2023
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Some nice properties that real numbers satisfies but Matrices don't.
11:26
Any square matrix can be written as sum of Symmetric and Skew Symmetric matrix and that too UNIQUELY
9:01
Tricks to find examples on Symmetric & Skew symmetric matrix. Diagonal entries of sk sym matrix = 0.
15:39
Can a non zero matrix be both symmetric as well as skew symmetric?
3:50
What can you say about determinant of a Skew Symmetric matrix of odd order? Is it Zero? Why?
6:45
Can we have a non-zero #matrix  which is #diagonal as well as skew-symmetric? #shorts
0:58
#shortcut to find #determinant of a #matrix using #properties . #mathematics #shorts
0:59
Orthogonal matrix & examples. Inverse, transpose, arithmetic operations between orthogonal matrices.
13:24
Rows & columns of orthogonal matrices are orthogonal. Moreover length of row & column vectors are 1.
10:26
Any 2 by 2 orthogonal matrix is either a rotation matrix or a reflection matrix.
8:50
Row / Column operations on a matrix is equivalent to Pre / Post Matrix Multiplication.
6:47
Example when (ab)^inverse is not equal to a^inverse*b^inverse
5:53
Linear Algebra Question on row reduced echelon form in GATE 2021
4:49
How Linear Combination concept evolved from your high school mathematics to Vectors spaces!
21:32
Solution to traffic problem using LINEAR ALGEBRA.
10:12
Linearly Independent and dependent vectors:: concept and examples
23:11
Subsets and Supersets of Linearly Independent and Linearly dependent sets.
11:19
Rank of a Matrix: Maximum number of linearly independent row or column vectors.(see pinned comment)
13:41
Existence of solution to System of Linear equations.
20:40
Matrix rank example (CSIR NET 2019 question - Linear algebra)
4:01
VECTOR SPACE: Looking at the Properties and an Example simultaneously.
29:16
Matrices and Vector Space Structure. Examples and Non-Examples.
18:13
Is R^2 always a vector space over R? One has to be careful before answering Yes
5:02
Tricks to determine whether a given subset of R^n is a subspace or not.
15:18
If {0} is the only linearly dependent set of V then the dimension of V is???
3:40
Example of a subset of R^2 which is not a subspace??
2:46
Number of elements in a Subspace are infinite!!
4:57
Examples on Subspaces and Non Subspaces of Matrix Space!
15:05
Examples of SubSpaces and Non SubSpaces of Polynomial Space
13:23
Is Addition, Scalar Multiplication, Intersection and Union of Subspaces is again a Subspace?
18:28
When is Union of Subspaces is again a subspace? Proof and Counterexample.
8:42
Spanning set of subset in Vector Space along with important results.
17:51
Basis and Dimension of a Vector space. How can one construct infinitely many basis subsets?!
28:17
Basis and Dimension for Symmetric Matrices of Order n. Precise as well as Shortcut proof!
21:01
Basis and Dimension for Skew Symmetric Matrices. Precise as well as Shortcut solution.
17:07
Basis and Dimension of Trace 0 and Other such type of Matrices.
14:27
An Example on Basis and Dimension of U, V, U intersection V and U + V of a polynomial space
8:48
Rank Nullity theorem for matrices.
14:32
Linear Algebra question on dimension of subspaces in GATE 2022 Exam
9:14
Coordinate vector with respect to given ordered basis. Is this a well defined concept??
12:17
Motivation to study Change of Basis Matrix along with an example and homework problem
18:23
What the word linear means in Linear Transformations. Concept, Examples and some nice Hints
19:27
What is and Why do we study Kernel of a linear transformation?
15:02
Examples on Image space of a linear transformation
13:59
Linear transformation is one-one function if and only if Kernel contains only singleton zero vector
8:04
Linear map is one one if and only if its onto if and only if its invertible iff bijective
10:25
Steps on how to find a Matrix corresponding to a Linear Transformation.
16:37
What are Eigenvalues and Eigenvectors? Concept and examples using linear transformations.
15:14
Steps to find eigenvalues and eigenvectors along with examples.
17:39
Eigenvalues and Eigenvectors for power of a Matrix?
8:12
Some Nice properties of Eigenvalues.
12:50
Determinant of a matrix is equal to product of eigenvalues. Proof and simple example.
5:38
Properties of Eigenvalues for scalar multiplication and scalar addition of matrices.
9:44
Does a #matrix always have #real  #eigenvalues ? #shorts
1:00
Can we have an #eigenvector corresponding to two different #eigenvalues ? #shorts
0:58
Example of an integral operator which has NO Eigenvalues!!
7:25
Eigenvalues and Eigenvectors of a polynomial
6:19
Relation between Eigenvalues and Eigenvectors of inverse of A and adjoint of A.
7:40
Linear algebra Question on Trace and Determinant of a matrix in GATE 2022 Examination
6:03
Algebraic multiplicity, Eigenspaces and Geometric multiplicity. Any connection between them?
14:47
Proof of - Geometric Multiplicity is less equal Algebraic Multiplicity
11:22
Similar matrices and the ten nice properties that they preserve.
19:44
What is, and importance of, diagonalizable matrices. Examples and uniqueness using examples.
14:41
Given eigenvalues and eigenvectors, how to find a matrix?
6:41
Cayley Hamilton Theorem: Its meaning and application in solving problems
12:13
Linear algebra question on Cayley-Hamilton Theorem in GATE 2022
2:33
Why do we need Inner Product? Motivation to study this topic!
15:09
Infinitely many examples and non-examples of Inner products on vector spaces.
15:33
Infinite examples on Inner Product on Polynomial Vector Space.
22:05
Linear Algebra Question on Non-Singularity and Nullity in GATE 2021 exam
5:13
Example of an inner product on Matrices which helps us to find angle and length.
18:23
Orthogonal Vectors are Linearly Independent vectors but not conversely. Counterexample as well.
11:48
Orthogonal Matrices may not be Orthogonal!!
4:27
Orthogonal and Orthonormal vectors and its connection with Linearly independent vectors!!
19:56
Motivation to study Gram- Schmidt orthogonalization process!
18:35
Gram Schmidt Orthogonalization process (Geometrically). Formula and examples.
29:02
Generalization of Generalized Pythagoras Theorem. (Pythagoras identity in Inner Product space)
10:45
Orthogonal Complement. Concept, Examples, Nice results and Some Tricks.
23:00
Linear Transformations : Geometrically
21:34
What are all subspaces of R2? Math job/ PhD Interview Question
9:15
How to define Orthogonal matrices: Geometrically |Math Interview (Job/ Ph.D)
6:47