"Eigenvectors... change at most by a scalar factor when that linear transformation is applied."
"I woke up today and I chose violence... we are going to be ranking every Shonen transformation power up."
"People pay for transformations, not information."
"His progressive growth and unpredictable transformations kept fans interested."
"That's what these revolutions are about, that's what these transformations are."
"Graph transformations: flip it over and shifting it up one."
"It's a time of breakups, personally and professionally, as Pluto brings buried things to the surface."
"That kind of idea of making transformations for expressions was a good model of how to think about mathematics."
"...it's amazing to see so many performers whose careers were salvaged thanks to their stark transformations..."
"So now we have these three things that can happen to an individual mesh or an object."
"The really cool thing about using this type of matrix is that you can multiply matrices together, and what you're gonna get is a combined transformation of one space into another space, and that is really, really powerful."
"You can use matrices to transform vectors between coordinate spaces."
"If W is one, you're transforming a point."
"If W is zero, you're transforming only the direction."
"Dragon Ball Heroes creates its own Canon with original transformations and characters."
"Jupiter moving into Gemini in 2024 signifies big transformations and financial gains for Scorpios."
"Visualizing matrix transformations: grid space and parallel lines."
"The transformations we do in geometric algebra for rotations and translations, they look exactly like the quaternion product, but they are really just combinations of two reflections."
"I'm excited for like any of the druid transformations."
"Ben Grim turns normal every year thanks to a serum created by Valaria... once a year he gets to experience what it's like to be a regular person."
"I don't think we have ever seen such a drastic shift in hatred to being beloved as quickly and intensely as we did with Raja."
"Stark and Baraggan have two of the greatest transformations in Bleach."
"It's not makeovers, it's shakeovers."
"They set it up in the movie with her turning like some dude into a celestial into a celestial but a diving into a tree and it's like okay so like that was your first time. Yeah, your second time is stopping a [ __ ] celestial."
"And when you think about this field, these are the great times in understanding great transformations."
"The real interesting thing is, either way we compose these transformations, they end up being rotations about some other point."
"The effects are really well done with the ghosts and face transformations."
"Despite the challenges and constraints, the Property Brothers continue to deliver awe-inspiring transformations."
"Piccolo's new transformation, known as 'orange Piccolo,' represents the massive buffer that the Namekian king needed to keep up with the rest of the Z Fighters."
"Ben's roster of alien transformations...takes an inch and gives you a mile of DNA to play with."
"Systems change with time by unitary transformation. That's the message. The unitary operators are the things which take you from one time step to another."
"Unexpected opportunities can shape our lives in remarkable ways."
"The connections we make in life can lead to profound transformations."
"...and there you have Bone Crusher in his robot mode."
"...and there you have Scavenger in his robot mode."
"And there you have scavenger in his alt mode."
"Man to get him into combined mode what we need to do make the suction and again just rotate this around just kind of bring all this up get it out of our way."
"And there you have Ricky oh in combine mode."
"Transformations have huge opportunities for narrative in ways that other mediums don't."
"This complex geological history challenges our understanding of Mars, painting it not as a static world but as one that has undergone significant transformations."
"A transformation is linear if it preserves addition and scalar multiplication."
"Transforms are used to translate, rotate, and scale entities."
"Mathematicians think about symmetry since about 1830 is in terms of transformations."
"Translations, reflections, and rotations will always preserve distance."
"Matrices are super useful for transformations and Unity defines many of the matrices involved in transforming from one space to another."
"Layers upon layers of mathematical transformations, not anything magical, just a lot of operations stacked together."
"In general, there is no unique way to write a given linear transformation as a composition of basic transformations."
"Thinking about linear transformations is often a much more convenient way to think about group elements."
"Reflections and rotations are going to preserve distance and angles."
"Rigid motions are transformations that do not change the size or the shape of a geometric object."
"Both reflections and rotations preserve length, so when you put them together, they will also preserve length."
"It is so important that you understand transformations."
"If you could just make a carbon copy of this parabola, you could just move it left and right."
"Transformations can be inverted; you can always transform back to the original location."
"We looked at the idea of symmetry, which is what we call the ability to apply transformations to an object that will leave it looking identical."
"Linear algebra can be thought of as the study of linear transformations."
"The most intuitive examples of general topological transformations are the deformations."