Scalar: A scalar is a single numerical value. It has magnitude but no direction. For instance, in mathematical terms, the number 5 or -3.2 are scalar values.
Vector: A vector is an ordered list of numbers. It can be visualized as a line segment in space that has both magnitude and direction. Mathematically, a vector is typically represented as a column (or sometimes row) of numbers (aka 1-D data)
Matrix: A matrix is a two-dimensional array of numbers. It can be visualized as a rectangular grid of numbers. A matrix has rows and columns, and its shape is often described by the number of rows by the number of columns, e.g., a 3x2 matrix has 3 rows and 2 columns.
Tensor: A tensor is a multi-dimensional array of numbers. While a scalar is 0-dimensional, a vector is 1-dimensional, and a matrix is 2-dimensional, a tensor can be 3-dimensional or more. For instance, a 3-dimensional tensor can be visualized as a cube of numbers.
Scalar: An example of a scalar is the current temperature. If it's 22°C right now, that's a single numerical value.
Vector: An example of a vector could be the average high temperatures forecasted for the next week. For instance, if the forecasted high temperatures for the next seven days are 22°C, 23°C, 24°C, 25°C, 26°C, 27°C, and 28°C, then the vector representation might be: [22, 23, 24, 25, 26, 27, 28]
Matrix: An example of a matrix is a grayscale image. The pixels of the image are represented as values between 0 (black) and 255 (white). The image's resolution, say 100x100 pixels, will determine the size of the matrix. Each entry in the matrix corresponds to the grayscale value of a pixel.
Tensor: A tensor example is a colored image. In the most common format, an image has three color channels: Red, Green, and Blue (RGB). Each channel can be thought of as a matrix (like the grayscale image), and the three matrices combined form a 3-dimensional tensor. If the image is of resolution 100x100 pixels, the tensor's shape would be 100x100x3, with each slice of size 100x100 representing one of the RGB channels.