Linear combinations
What is linear combinations? When we study linear algebra, we keep running into the idea of “linearity” in a few core ways. Each one focuses on a different kind of object: Today, we’ll start with linear combinations. What is a…
B Buffs
Linear Dependence and Linear Independence
In our previous post, we explored Linear Combinations—the art of mixing vectors together to reach new points in space. It showed us what is possible to build. But in mathematics, as in business, just knowing what is possible isn’t enough;…
Understanding the Basis
In linear algebra, we often want to find the simplest set of building blocks that can construct every single element in a space without any redundancy. This set is called a Basis. We are going to define a Basis using…
Why We Obsess Over Matrices: Turning Calculus into Arithmetic
We have already explored the building blocks of Linear Algebra: first, Linear Combinations (understanding individual vectors), and second, Linear Independence (understanding sets of vectors). Now, we are ready to dive into the “verbs” of Linear Algebra: Linear Transformations and The…
Native English Expressions | Ep.6
Do you feel lost when listening to native speakers? It’s likely because textbook English isn’t enough. Welcome to Native Expressions Ep.6. Real conversations are full of idioms, phrasal verbs, and cultural nuances. This series curates authentic expressions directly from podcasts and YouTube…
Oxford 5000: 50 Words | Beginner | EP.12
Are you finding it hard to tackle the Oxford 5000 word list on your own? Welcome to Oxford 5000 Beginner Ep.12. These are the essential words you need for fluent communication. This series breaks them down step-by-step, categorized by difficulty…
Native English Expressions | Ep.5
Do you feel lost when listening to native speakers? It’s likely because textbook English isn’t enough. Welcome to Native Expressions Ep.5. Real conversations are full of idioms, phrasal verbs, and cultural nuances. This series curates authentic expressions directly from podcasts and YouTube…
Oxford 5000: 50 Words | Intermediate | EP.11
Are you finding it hard to tackle the Oxford 5000 word list on your own? Welcome to Oxford 5000 Intermediate Ep.11. These are the essential words you need for fluent communication. This series breaks them down step-by-step, categorized by difficulty level, to…
Native English Expressions | Ep.4
Do you feel lost when listening to native speakers? It’s likely because textbook English isn’t enough. Welcome to Native Expressions Ep.4. Real conversations are full of idioms, phrasal verbs, and cultural nuances. This series curates authentic expressions directly from podcasts and YouTube…
Oxford 5000: 50 Words | Beginner | EP.11
Are you finding it hard to tackle the Oxford 5000 word list on your own? Welcome to Oxford 5000 Beginner Ep.11. These are the essential words you need for fluent communication. This series breaks them down step-by-step, categorized by difficulty…